Cremona's table of elliptic curves

27600 = 2⁴ · 3 · 5² · 23

Class	r	Atkin-Lehner	Eigenvalues
27600a (6 curves)	1	2+ 3+ 5+ 23+	2+ 3+ 5+  0  4  2 -2 -4
Curve Equation t Generators 27600a1 [0,-1,0,-3234383,-2237825238] 2 [-4265880508254932225793472884658:-379401612257874198171198316:4109712884836533675488404007] 27600a2 [0,-1,0,-3234508,-2237643488] 4 [-160716162009204:-18106398388408:153388121977] 27600a3 [0,-1,0,-2924008,-2684763488] 2 [541183984274118489448605318:-4878640357946165792402842189:258613723899409244111416] 27600a4 [0,-1,0,-3547008,-1778893488] 4 [-81940968:-374329836:148877] 27600a5 [0,-1,0,9677992,-11935693488] 2 [11332155106140722:-11909148212659190706:10260751717] 27600a6 [0,-1,0,-21772008,37732906512] 2 [288:177444:1]
27600b (4 curves)	1	2+ 3+ 5+ 23+	2+ 3+ 5+  0 -4 -2 -2  0
Curve Equation t Generators 27600b1 [0,-1,0,-2908,61312] 2 [33:14:1] 27600b2 [0,-1,0,-3408,39312] 4 [-48:300:1] 27600b3 [0,-1,0,11592,279312] 2 [2:550:1] 27600b4 [0,-1,0,-26408,-1616688] 2 [-94:162:1]
27600c (2 curves)	1	2+ 3+ 5+ 23+	2+ 3+ 5+  2  2  2  4  0
Curve Equation t Generators 27600c1 [0,-1,0,-1608,35712] 2 [6:162:1] 27600c2 [0,-1,0,-28608,1871712] 2 [92:100:1]
27600d (1 curve)	1	2+ 3+ 5+ 23+	2+ 3+ 5+  3  2 -2  1 -6
Curve Equation t Generators 27600d1 [0,-1,0,-7033,6776437] 1 [2308:164025:64]
27600e (1 curve)	1	2+ 3+ 5+ 23+	2+ 3+ 5+ -3 -2 -1 -8  5
Curve Equation t Generators 27600e1 [0,-1,0,-33,477] 1 [-4:23:1]
27600f (1 curve)	0	2+ 3+ 5+ 23-	2+ 3+ 5+  1  0  4  1  0
Curve Equation t 27600f1 [0,-1,0,367,-15363] 1
27600g (2 curves)	0	2+ 3+ 5+ 23-	2+ 3+ 5+  2  0 -2  4  6
Curve Equation t 27600g1 [0,-1,0,92,1312] 2 27600g2 [0,-1,0,-1408,19312] 2
27600h (2 curves)	0	2+ 3+ 5+ 23-	2+ 3+ 5+  2  2 -2  8 -4
Curve Equation t 27600h1 [0,-1,0,2992,106512] 2 27600h2 [0,-1,0,-24008,1186512] 2
27600i (2 curves)	0	2+ 3+ 5+ 23-	2+ 3+ 5+ -2  0 -2 -8 -6
Curve Equation t 27600i1 [0,-1,0,-72708,-7589088] 2 27600i2 [0,-1,0,-1166208,-484355088] 2
27600j (4 curves)	0	2+ 3+ 5+ 23-	2+ 3+ 5+  4 -4 -6  2 -4
Curve Equation t 27600j1 [0,-1,0,-783,7062] 2 27600j2 [0,-1,0,-3908,-86688] 4 27600j3 [0,-1,0,3592,-386688] 4 27600j4 [0,-1,0,-61408,-5836688] 2
27600k (2 curves)	0	2+ 3+ 5+ 23-	2+ 3+ 5+  4  6  4 -2  0
Curve Equation t 27600k1 [0,-1,0,1592,-82688] 2 27600k2 [0,-1,0,-21408,-1094688] 2
27600l (4 curves)	0	2+ 3+ 5+ 23-	2+ 3+ 5+ -4  4  2  2  0
Curve Equation t 27600l1 [0,-1,0,-5183,145362] 2 27600l2 [0,-1,0,-5308,138112] 4 27600l3 [0,-1,0,6192,644112] 2 27600l4 [0,-1,0,-18808,-833888] 2
27600m (1 curve)	2	2+ 3+ 5- 23+	2+ 3+ 5- -1 -3 -5  2 -5
Curve Equation t Generators 27600m1 [0,-1,0,-6208,-139088] 1 [-58:150:1]&[-47:216:1]
27600n (2 curves)	0	2+ 3+ 5- 23+	2+ 3+ 5- -2  4  0 -2  4
Curve Equation t 27600n1 [0,-1,0,252,2592] 2 27600n2 [0,-1,0,-2048,30192] 2
27600o (2 curves)	1	2+ 3+ 5- 23-	2+ 3+ 5-  0  0  0 -4 -2
Curve Equation t Generators 27600o1 [0,-1,0,-25708,1594912] 2 [141:868:1] 27600o2 [0,-1,0,-23208,1914912] 2 [-58:1750:1]
27600p (1 curve)	1	2+ 3+ 5- 23-	2+ 3+ 5-  3  0 -2 -3 -6
Curve Equation t Generators 27600p1 [0,-1,0,-208,1312] 1 [12:-20:1]
27600q (1 curve)	1	2+ 3+ 5- 23-	2+ 3+ 5- -3  3  7  6 -3
Curve Equation t Generators 27600q1 [0,-1,0,-74208,-2603088] 1 [342:3450:1]
27600r (1 curve)	1	2+ 3+ 5- 23-	2+ 3+ 5- -3 -5  3 -6  1
Curve Equation t Generators 27600r1 [0,-1,0,-19525408,32517768112] 1 [175246:73338858:1]
27600s (4 curves)	0	2+ 3- 5+ 23+	2+ 3- 5+  0  0  2  6  0
Curve Equation t 27600s1 [0,1,0,-98908,76602188] 2 27600s2 [0,1,0,-3379408,2379513188] 4 27600s3 [0,1,0,-5242408,-537944812] 2 27600s4 [0,1,0,-54004408,152735763188] 2
27600t (2 curves)	0	2+ 3- 5+ 23+	2+ 3- 5+  0 -2  0 -6 -8
Curve Equation t 27600t1 [0,1,0,-801008,-288018012] 2 27600t2 [0,1,0,-12968008,-17978836012] 2
27600u (1 curve)	0	2+ 3- 5+ 23+	2+ 3- 5+  3  3 -7 -6 -3
Curve Equation t 27600u1 [0,1,0,-2968,-22012] 1
27600v (1 curve)	0	2+ 3- 5+ 23+	2+ 3- 5+  3 -5 -3  6  1
Curve Equation t 27600v1 [0,1,0,-488135208,4063744743588] 1
27600w (1 curve)	0	2+ 3- 5+ 23+	2+ 3- 5+  3  6  2 -3  6
Curve Equation t 27600w1 [0,1,0,-5033,-139437] 1
27600x (1 curve)	0	2+ 3- 5+ 23+	2+ 3- 5+ -3  0  2  3 -6
Curve Equation t 27600x1 [0,1,0,-5208,153588] 1
27600y (4 curves)	0	2+ 3- 5+ 23+	2+ 3- 5+ -4  0  2  2  4
Curve Equation t 27600y1 [0,1,0,-108,-4212] 2 27600y2 [0,1,0,-4608,-121212] 4 27600y3 [0,1,0,-7608,52788] 2 27600y4 [0,1,0,-73608,-7711212] 2
27600z (1 curve)	1	2+ 3- 5+ 23-	2+ 3- 5+  1 -3  5 -2 -5
Curve Equation t Generators 27600z1 [0,1,0,-248,-1212] 1 [-8:18:1]
27600ba (1 curve)	1	2+ 3- 5+ 23-	2+ 3- 5+ -3  4  0 -3  4
Curve Equation t Generators 27600ba1 [0,1,0,190367,-140529637] 1 [638:15525:1]
27600bb (2 curves)	1	2+ 3- 5- 23+	2+ 3- 5-  0  0  0  4 -2
Curve Equation t Generators 27600bb1 [0,1,0,-1028,12348] 2 [-2:120:1] 27600bb2 [0,1,0,-928,14948] 2 [8:-90:1]
27600bc (2 curves)	0	2+ 3- 5- 23-	2+ 3- 5-  2  4  0  2  4
Curve Equation t 27600bc1 [0,1,0,6292,336588] 2 27600bc2 [0,1,0,-51208,3671588] 2
27600bd (1 curve)	0	2+ 3- 5- 23-	2+ 3- 5-  3 -2  1  8  5
Curve Equation t 27600bd1 [0,1,0,-833,57963] 1
27600be (4 curves)	0	2- 3+ 5+ 23+	2- 3+ 5+  0  0  2 -2  8
Curve Equation t 27600be1 [0,-1,0,1192,-15888] 2 27600be2 [0,-1,0,-6808,-143888] 4 27600be3 [0,-1,0,-42808,3312112] 2 27600be4 [0,-1,0,-98808,-11919888] 2
27600bf (2 curves)	0	2- 3+ 5+ 23+	2- 3+ 5+  0  0  6 -2 -6
Curve Equation t 27600bf1 [0,-1,0,-533,4812] 2 27600bf2 [0,-1,0,92,14812] 2
27600bg (4 curves)	0	2- 3+ 5+ 23+	2- 3+ 5+  0  0 -6 -2  0
Curve Equation t 27600bg1 [0,-1,0,-1796408,1647123312] 2 27600bg2 [0,-1,0,-34564408,78193171312] 4 27600bg3 [0,-1,0,-40452408,49742355312] 2 27600bg4 [0,-1,0,-552964408,5005066771312] 2
27600bh (2 curves)	0	2- 3+ 5+ 23+	2- 3+ 5+ -2 -2  2  0 -8
Curve Equation t 27600bh1 [0,-1,0,-9111008,726743584512] 2 27600bh2 [0,-1,0,-1268823008,17178582304512] 2
27600bi (2 curves)	0	2- 3+ 5+ 23+	2- 3+ 5+ -2  6  2  0  0
Curve Equation t 27600bi1 [0,-1,0,-608,-12288] 2 27600bi2 [0,-1,0,-12608,-540288] 2
27600bj (2 curves)	0	2- 3+ 5+ 23+	2- 3+ 5+ -2 -6  2  0  4
Curve Equation t 27600bj1 [0,-1,0,68592,16293312] 2 27600bj2 [0,-1,0,-699408,197541312] 2
27600bk (1 curve)	0	2- 3+ 5+ 23+	2- 3+ 5+  3 -2  2 -5  2
Curve Equation t 27600bk1 [0,-1,0,11867,690637] 1
27600bl (1 curve)	0	2- 3+ 5+ 23+	2- 3+ 5+  3  3  3  4  3
Curve Equation t 27600bl1 [0,-1,0,-1128,-13968] 1
27600bm (1 curve)	0	2- 3+ 5+ 23+	2- 3+ 5+  3 -5 -1 -8 -1
Curve Equation t 27600bm1 [0,-1,0,-244168,-46357328] 1
27600bn (2 curves)	0	2- 3+ 5+ 23+	2- 3+ 5+  4 -2 -4  6  4
Curve Equation t 27600bn1 [0,-1,0,-5008,248512] 2 27600bn2 [0,-1,0,-97008,11656512] 2
27600bo (1 curve)	0	2- 3+ 5+ 23+	2- 3+ 5+ -5  0 -4  3  4
Curve Equation t 27600bo1 [0,-1,0,19173467,-14119067063] 1
27600bp (1 curve)	0	2- 3+ 5+ 23+	2- 3+ 5+ -5  3  5  6  1
Curve Equation t 27600bp1 [0,-1,0,-10208,-281088] 1
27600bq (1 curve)	1	2- 3+ 5+ 23-	2- 3+ 5+  1 -4  0 -5  0
Curve Equation t Generators 27600bq1 [0,-1,0,-292533,60997437] 1 [372:1875:1]
27600br (1 curve)	1	2- 3+ 5+ 23-	2- 3+ 5+  1  5 -3 -2  3
Curve Equation t Generators 27600br1 [0,-1,0,-2208,-39168] 1 [-27:6:1]
27600bs (2 curves)	1	2- 3+ 5+ 23-	2- 3+ 5+ -2  2  6  4  0
Curve Equation t Generators 27600bs1 [0,-1,0,1592,-220688] 2 [106:1062:1] 27600bs2 [0,-1,0,-46408,-3676688] 2 [932:27600:1]
27600bt (1 curve)	1	2- 3+ 5+ 23-	2- 3+ 5+ -3  1 -1  4 -7
Curve Equation t Generators 27600bt1 [0,-1,0,-305208,-64091088] 1 [-342:414:1]
27600bu (2 curves)	1	2- 3+ 5+ 23-	2- 3+ 5+  4  2  0 -2  0
Curve Equation t Generators 27600bu1 [0,-1,0,66592,3309312] 2 [-38:850:1] 27600bu2 [0,-1,0,-301408,28333312] 2 [7322:624750:1]
27600bv (2 curves)	1	2- 3+ 5- 23+	2- 3+ 5- -2  0  4  2  4
Curve Equation t Generators 27600bv1 [0,-1,0,-568,6832] 2 [12:-40:1] 27600bv2 [0,-1,0,-9768,374832] 2 [-78:810:1]
27600bw (1 curve)	1	2- 3+ 5- 23+	2- 3+ 5-  3  1 -3  0  5
Curve Equation t Generators 27600bw1 [0,-1,0,-34608,-1562688] 1 [-78:810:1]
27600bx (1 curve)	1	2- 3+ 5- 23+	2- 3+ 5- -3 -2 -3  0 -1
Curve Equation t Generators 27600bx1 [0,-1,0,-45333,3731037] 1 [92:575:1]
27600by (1 curve)	1	2- 3+ 5- 23+	2- 3+ 5- -3  5  1 -4  3
Curve Equation t Generators 27600by1 [0,-1,0,-3708,85212] 1 [234:243:8]
27600bz (2 curves)	1	2- 3+ 5- 23+	2- 3+ 5- -5  0  2  3 -2
Curve Equation t Generators 27600bz1 [0,-1,0,369192,64457712] 1 [-148:2560:1] 27600bz2 [0,-1,0,-8324808,9356604912] 1 [-5685628:255852544:2197]
27600ca (2 curves)	0	2- 3+ 5- 23-	2- 3+ 5-  0  0 -4  0  2
Curve Equation t 27600ca1 [0,-1,0,-2208,-17088] 2 27600ca2 [0,-1,0,7792,-137088] 2
27600cb (2 curves)	0	2- 3+ 5- 23-	2- 3+ 5-  1  0  2  3 -2
Curve Equation t 27600cb1 [0,-1,0,-10208,1158912] 1 27600cb2 [0,-1,0,-1210208,512838912] 1
27600cc (2 curves)	0	2- 3+ 5- 23-	2- 3+ 5-  1  3 -1  6  1
Curve Equation t 27600cc1 [0,-1,0,-437208,-111107088] 1 27600cc2 [0,-1,0,-1067208,271932912] 1
27600cd (2 curves)	0	2- 3+ 5- 23-	2- 3+ 5-  1  6  5  0 -5
Curve Equation t 27600cd1 [0,-1,0,7467,-8163] 1 27600cd2 [0,-1,0,-100533,13232637] 1
27600ce (1 curve)	0	2- 3+ 5- 23-	2- 3+ 5-  3 -1  1  0  5
Curve Equation t 27600ce1 [0,-1,0,-708,2412] 1
27600cf (1 curve)	0	2- 3+ 5- 23-	2- 3+ 5-  5 -5  1  0  7
Curve Equation t 27600cf1 [0,-1,0,-332208,-41897088] 1
27600cg (2 curves)	1	2- 3- 5+ 23+	2- 3- 5+  0  2 -4 -6  8
Curve Equation t Generators 27600cg1 [0,1,0,-98008,11827988] 2 [52:2622:1] 27600cg2 [0,1,0,-1570008,756659988] 2 [1398:36000:1]
27600ch (6 curves)	1	2- 3- 5+ 23+	2- 3- 5+  0 -4  2  6 -4
Curve Equation t Generators 27600ch1 [0,1,0,-168008,-29136012] 2 [628:10650:1] 27600ch2 [0,1,0,-2760008,-1765776012] 4 [4084:234726:1] 27600ch3 [0,1,0,-2832008,-1668864012] 4 [99674276:5721494814:24389] 27600ch4 [0,1,0,-44160008,-112966176012] 2 [54232156:-1231434366:6859] 27600ch5 [0,1,0,3515992,-8080344012] 2 [51595243813092036:3340033842401234454:13496571664129] 27600ch6 [0,1,0,-10332008,10946135988] 2 [294714:-17835000:343]
27600ci (2 curves)	1	2- 3- 5+ 23+	2- 3- 5+ -1  0 -2 -3 -2
Curve Equation t Generators 27600ci1 [0,1,0,-408,9108] 1 [54:384:1] 27600ci2 [0,1,0,-48408,4083348] 1 [134:144:1]
27600cj (2 curves)	1	2- 3- 5+ 23+	2- 3- 5+ -1  0  4  3  4
Curve Equation t Generators 27600cj1 [0,1,0,1467,18063] 1 [3:150:1] 27600cj2 [0,1,0,-34533,2484063] 1 [63:750:1]
27600ck (2 curves)	1	2- 3- 5+ 23+	2- 3- 5+ -1  3  1 -6  1
Curve Equation t Generators 27600ck1 [0,1,0,-17488,-895852] 1 [-76:6:1] 27600ck2 [0,1,0,-42688,2158388] 1 [44:606:1]
27600cl (2 curves)	1	2- 3- 5+ 23+	2- 3- 5+ -1  6 -5  0 -5
Curve Equation t Generators 27600cl1 [0,1,0,186667,-647037] 1 [22:1863:1] 27600cl2 [0,1,0,-2513333,1649052963] 1 [-412454:18579009:343]
27600cm (4 curves)	1	2- 3- 5+ 23+	2- 3- 5+  2  0 -2  0 -2
Curve Equation t Generators 27600cm1 [0,1,0,-14208,-686412] 2 [234:2976:1] 27600cm2 [0,1,0,-230208,-42590412] 2 [684:10974:1] 27600cm3 [0,1,0,75792,-1370412] 2 [191324:5026650:343] 27600cm4 [0,1,0,-308208,-11354412] 2 [2921596804:45039282294:4173281]
27600cn (2 curves)	1	2- 3- 5+ 23+	2- 3- 5+ -2 -4  6 -4 -2
Curve Equation t Generators 27600cn1 [0,1,0,-208,5588] 2 [2:72:1] 27600cn2 [0,1,0,-6208,185588] 2 [52:78:1]
27600co (1 curve)	1	2- 3- 5+ 23+	2- 3- 5+ -3 -1 -1  0  5
Curve Equation t Generators 27600co1 [0,1,0,-28,8] 1 [-1:6:1]
27600cp (4 curves)	1	2- 3- 5+ 23+	2- 3- 5+  4  4  2 -6 -8
Curve Equation t Generators 27600cp1 [0,1,0,3592,7188] 2 [22:312:1] 27600cp2 [0,1,0,-14408,43188] 4 [172:1638:1] 27600cp3 [0,1,0,-152408,-22864812] 2 [18444:374374:27] 27600cp4 [0,1,0,-164408,25543188] 2 [93996:366834:343]
27600cq (4 curves)	1	2- 3- 5+ 23+	2- 3- 5+  4 -4 -6  2  4
Curve Equation t Generators 27600cq1 [0,1,0,182592,-18844812] 2 [138:3000:1] 27600cq2 [0,1,0,-875408,-164848812] 4 [-638:11592:1] 27600cq3 [0,1,0,-6625408,6447651188] 4 [-2197:102000:1] 27600cq4 [0,1,0,-12053408,-16104676812] 2 [-1988:2142:1]
27600cr (4 curves)	1	2- 3- 5+ 23+	2- 3- 5+ -4  0 -2 -6 -2
Curve Equation t Generators 27600cr1 [0,1,0,-4133,68238] 2 [-62:300:1] 27600cr2 [0,1,0,11492,474488] 2 [143:2250:1] 27600cr3 [0,1,0,-304133,64455738] 2 [-3174:268100:27] 27600cr4 [0,1,0,-303508,64734488] 2 [343:1050:1]
27600cs (1 curve)	1	2- 3- 5+ 23+	2- 3- 5+ -5  2  6 -1 -2
Curve Equation t Generators 27600cs1 [0,1,0,-40133,-3530637] 1 [238:675:1]
27600ct (1 curve)	1	2- 3- 5+ 23+	2- 3- 5+ -5 -5 -1  0  7
Curve Equation t Generators 27600ct1 [0,1,0,-13288,-340492] 1 [-76:486:1]
27600cu (2 curves)	0	2- 3- 5+ 23-	2- 3- 5+  0 -2  0 -6 -4
Curve Equation t 27600cu1 [0,1,0,53592,4939188] 2 27600cu2 [0,1,0,-314408,46891188] 2
27600cv (4 curves)	0	2- 3- 5+ 23-	2- 3- 5+  0  4  6  6 -4
Curve Equation t 27600cv1 [0,1,0,-241408,45387188] 2 27600cv2 [0,1,0,-369408,-8116812] 4 27600cv3 [0,1,0,1470592,-63316812] 2 27600cv4 [0,1,0,-4257408,-3375124812] 2
27600cw (4 curves)	0	2- 3- 5+ 23-	2- 3- 5+  0 -4  2 -2  0
Curve Equation t 27600cw1 [0,1,0,-5008,-76012] 2 27600cw2 [0,1,0,-37008,2675988] 4 27600cw3 [0,1,0,2992,8195988] 4 27600cw4 [0,1,0,-589008,173795988] 2
27600cx (1 curve)	0	2- 3- 5+ 23-	2- 3- 5+  3 -2  3  0 -1
Curve Equation t 27600cx1 [0,1,0,-1813,29123] 1
27600cy (1 curve)	0	2- 3- 5+ 23-	2- 3- 5+  3  5 -1  4  3
Curve Equation t 27600cy1 [0,1,0,-92708,10466088] 1
27600cz (1 curve)	0	2- 3- 5+ 23-	2- 3- 5+ -3  1  3  0  5
Curve Equation t 27600cz1 [0,1,0,-865208,-197066412] 1
27600da (1 curve)	0	2- 3- 5+ 23-	2- 3- 5+ -3  2  2  7  6
Curve Equation t 27600da1 [0,1,0,-21133,-1664137] 1
27600db (1 curve)	0	2- 3- 5+ 23-	2- 3- 5+ -3  4  0  3  8
Curve Equation t 27600db1 [0,1,0,-533,-13437] 1
27600dc (2 curves)	0	2- 3- 5+ 23-	2- 3- 5+  5  0 -2 -3 -2
Curve Equation t 27600dc1 [0,1,0,9229792,8075673588] 1 27600dc2 [0,1,0,-208120208,1169159373588] 1
27600dd (2 curves)	0	2- 3- 5- 23+	2- 3- 5-  0  0  4  0  2
Curve Equation t 27600dd1 [0,1,0,-88,-172] 2 27600dd2 [0,1,0,312,-972] 2
27600de (1 curve)	0	2- 3- 5- 23+	2- 3- 5- -1  5  3  2  3
Curve Equation t 27600de1 [0,1,0,-55208,-5006412] 1
27600df (1 curve)	0	2- 3- 5- 23+	2- 3- 5-  3  1  1 -4 -7
Curve Equation t 27600df1 [0,1,0,-12208,-517612] 1
27600dg (2 curves)	1	2- 3- 5- 23-	2- 3- 5-  2  0 -4 -2  4
Curve Equation t Generators 27600dg1 [0,1,0,-14208,825588] 2 [42:-552:1] 27600dg2 [0,1,0,-244208,46365588] 2 [-92:8250:1]
27600dh (1 curve)	1	2- 3- 5- 23-	2- 3- 5- -3  3 -3 -4  3
Curve Equation t Generators 27600dh1 [0,1,0,-28208,-1802412] 1 [-92:150:1]
27600di (1 curve)	1	2- 3- 5- 23-	2- 3- 5- -3 -5  1  8 -1
Curve Equation t Generators 27600di1 [0,1,0,-6104208,-5806874412] 1 [-1428:138:1]
27600dj (1 curve)	1	2- 3- 5- 23-	2- 3- 5-  5  3 -5 -6  1
Curve Equation t Generators 27600dj1 [0,1,0,-408,-2412] 1 [-12:30:1]

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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