Cremona's table of elliptic curves

8400 = 2⁴ · 3 · 5² · 7

Class	r	Atkin-Lehner	Eigenvalues
8400a (4 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  0 -2 -2  0
Curve Equation t Generators 8400a1 [0,-1,0,-383,-738] 2 [-2:4:1] 8400a2 [0,-1,0,-3508,80512] 4 [12:200:1] 8400a3 [0,-1,0,-56008,5120512] 4 [-268:900:1] 8400a4 [0,-1,0,-1008,190512] 2 [-18:450:1]
8400b (1 curve)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  1 -4 -2  4
Curve Equation t Generators 8400b1 [0,-1,0,-68,-633] 1 [143:1701:1]
8400c (6 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  4  2 -2  4
Curve Equation t Generators 8400c1 [0,-1,0,-4383,-110238] 2 [9668:104225:64] 8400c2 [0,-1,0,-4508,-103488] 4 [-44:88:1] 8400c3 [0,-1,0,-17008,746512] 4 [-128:900:1] 8400c4 [0,-1,0,5992,-523488] 2 [698:6479:8] 8400c5 [0,-1,0,-262008,51706512] 2 [216:2268:1] 8400c6 [0,-1,0,27992,3986512] 2 [-78:1150:1]
8400d (4 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+ -4  2  6  0
Curve Equation t Generators 8400d1 [0,-1,0,-7908,273312] 2 [53:16:1] 8400d2 [0,-1,0,-8408,237312] 4 [-68:700:1] 8400d3 [0,-1,0,-43408,-3262688] 2 [-118:450:1] 8400d4 [0,-1,0,18592,1425312] 2 [-14:1078:1]
8400e (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  0  2 -6  4
Curve Equation t 8400e1 [0,-1,0,217,10062] 2 8400e2 [0,-1,0,-5908,169312] 4 8400e3 [0,-1,0,-16408,-586688] 2 8400e4 [0,-1,0,-93408,11019312] 2
8400f (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  0 -6  2 -4
Curve Equation t 8400f1 [0,-1,0,-183,-6138] 2 8400f2 [0,-1,0,-6308,-189888] 4 8400f3 [0,-1,0,-100808,-12285888] 2 8400f4 [0,-1,0,-9808,48112] 2
8400g (1 curve)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  2  5  3  8
Curve Equation t 8400g1 [0,-1,0,-8,-48] 1
8400h (1 curve)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  3  2  0 -2
Curve Equation t 8400h1 [0,-1,0,-28,-53] 1
8400i (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  4 -2  2  0
Curve Equation t 8400i1 [0,-1,0,217,-438] 2 8400i2 [0,-1,0,-908,-2688] 4 8400i3 [0,-1,0,-11408,-464688] 2 8400i4 [0,-1,0,-8408,297312] 4
8400j (6 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7- -4  2  6 -4
Curve Equation t 8400j1 [0,-1,0,-18383,-953238] 2 8400j2 [0,-1,0,-18508,-939488] 4 8400j3 [0,-1,0,-43008,2098512] 4 8400j4 [0,-1,0,3992,-3099488] 4 8400j5 [0,-1,0,-610008,183538512] 2 8400j6 [0,-1,0,131992,14698512] 2
8400k (1 curve)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7- -5 -2 -4 -6
Curve Equation t 8400k1 [0,-1,0,-845208,299548287] 1
8400l (1 curve)	0	2+ 3+ 5- 7+	2+ 3+ 5- 7+  3  2 -4  2
Curve Equation t 8400l1 [0,-1,0,15792,-1011213] 1
8400m (2 curves)	1	2+ 3+ 5- 7-	2+ 3+ 5- 7- -2  2  0 -2
Curve Equation t Generators 8400m1 [0,-1,0,-15428,742752] 2 [52:280:1] 8400m2 [0,-1,0,-15328,752752] 2 [46:378:1]
8400n (2 curves)	1	2+ 3+ 5- 7-	2+ 3+ 5- 7- -2  2  0  6
Curve Equation t Generators 8400n1 [0,-1,0,-708,-5088] 2 [41:182:1] 8400n2 [0,-1,0,1792,-35088] 2 [38:294:1]
8400o (1 curve)	1	2+ 3+ 5- 7-	2+ 3+ 5- 7- -2 -3 -5 -4
Curve Equation t Generators 8400o1 [0,-1,0,4941792,-7363325088] 1 [1292:34300:1]
8400p (1 curve)	1	2+ 3+ 5- 7-	2+ 3+ 5- 7- -3  0 -2  8
Curve Equation t Generators 8400p1 [0,-1,0,-208,-6713] 1 [67:525:1]
8400q (1 curve)	1	2+ 3+ 5- 7-	2+ 3+ 5- 7-  5  4  2 -4
Curve Equation t Generators 8400q1 [0,-1,0,-308,2187] 1 [11:3:1]
8400r (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  0  2 -6  4
Curve Equation t 8400r1 [0,1,0,-183,888] 2 8400r2 [0,1,0,-308,-612] 4 8400r3 [0,1,0,-3808,-91612] 2 8400r4 [0,1,0,1192,-3612] 2
8400s (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  0 -6  2 -4
Curve Equation t 8400s1 [0,1,0,-699783,225041688] 2 8400s2 [0,1,0,-777908,171604188] 4 8400s3 [0,1,0,-5065408,-4261670812] 2 8400s4 [0,1,0,2259592,1186129188] 2
8400t (1 curve)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+ -2  3  5 -4
Curve Equation t 8400t1 [0,1,0,197672,-58827532] 1
8400u (1 curve)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+ -3  0  2  8
Curve Equation t 8400u1 [0,1,0,-8,-57] 1
8400v (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  4  6  2  8
Curve Equation t 8400v1 [0,1,0,-1783,27188] 2 8400v2 [0,1,0,-4908,-97812] 4 8400v3 [0,1,0,-72408,-7522812] 2 8400v4 [0,1,0,12592,-622812] 4
8400w (6 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+ -4  2 -2 -4
Curve Equation t 8400w1 [0,1,0,-383,-12012] 2 8400w2 [0,1,0,-10508,-417012] 4 8400w3 [0,1,0,-168008,-26562012] 2 8400w4 [0,1,0,-15008,-30012] 4 8400w5 [0,1,0,-162008,24959988] 2 8400w6 [0,1,0,59992,-180012] 2
8400x (1 curve)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  5 -4 -2 -4
Curve Equation t 8400x1 [0,1,0,-7708,257963] 1
8400y (4 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  0 -2 -2 -4
Curve Equation t Generators 8400y1 [0,1,0,-908,10188] 2 [27:78:1] 8400y2 [0,1,0,-1408,-2812] 4 [-16:126:1] 8400y3 [0,1,0,-16408,-812812] 2 [148:150:1] 8400y4 [0,1,0,5592,-16812] 2 [18:300:1]
8400z (1 curve)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  3 -2  4  2
Curve Equation t Generators 8400z1 [0,1,0,632,-7837] 1 [29:189:1]
8400ba (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  2 -5 -3  8
Curve Equation t Generators 8400ba1 [0,1,0,-208,-6412] 1 [22:12:1]
8400bb (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -2 -2  0 -2
Curve Equation t Generators 8400bb1 [0,1,0,-385708,92072588] 2 [-142:12000:1] 8400bb2 [0,1,0,-383208,93327588] 2 [312:2058:1]
8400bc (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -2 -2  0  6
Curve Equation t Generators 8400bc1 [0,1,0,-28,-52] 2 [7:12:1] 8400bc2 [0,1,0,72,-252] 2 [8:30:1]
8400bd (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  3 -2  0 -2
Curve Equation t Generators 8400bd1 [0,1,0,-708,-8037] 1 [33:75:1]
8400be (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -5  2  4 -6
Curve Equation t Generators 8400be1 [0,1,0,-33808,2382863] 1 [113:135:1]
8400bf (1 curve)	0	2+ 3- 5- 7-	2+ 3- 5- 7-  1  4  2  4
Curve Equation t 8400bf1 [0,1,0,-1708,-82537] 1
8400bg (1 curve)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+  1  2  0 -6
Curve Equation t 8400bg1 [0,-1,0,1042,5787] 1
8400bh (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+ -2 -1  3  0
Curve Equation t 8400bh1 [0,-1,0,352,175872] 1 8400bh2 [0,-1,0,-1750208,891798912] 1
8400bi (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+ -2 -4 -6 -6
Curve Equation t 8400bi1 [0,-1,0,-101533,-8245688] 2 8400bi2 [0,-1,0,289092,-56683188] 2
8400bj (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+ -2  6  4  4
Curve Equation t 8400bj1 [0,-1,0,-33,312] 2 8400bj2 [0,-1,0,-908,10812] 2
8400bk (4 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+  4  2  6  0
Curve Equation t 8400bk1 [0,-1,0,-1408,13312] 2 8400bk2 [0,-1,0,-9408,-338688] 4 8400bk3 [0,-1,0,-149408,-22178688] 2 8400bk4 [0,-1,0,2592,-1154688] 2
8400bl (6 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+  4 -6 -2  4
Curve Equation t 8400bl1 [0,-1,0,-1608,-54288] 2 8400bl2 [0,-1,0,-33608,-2358288] 4 8400bl3 [0,-1,0,-537608,-151542288] 2 8400bl4 [0,-1,0,-41608,-1142288] 4 8400bl5 [0,-1,0,-365608,84393712] 2 8400bl6 [0,-1,0,154392,-8982288] 2
8400bm (1 curve)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -1 -4 -2  4
Curve Equation t Generators 8400bm1 [0,-1,0,2,7] 1 [1:3:1]
8400bn (2 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7-  2 -4 -2 -2
Curve Equation t Generators 8400bn1 [0,-1,0,-14133,-641988] 2 [605072:2814125:4096] 8400bn2 [0,-1,0,-13508,-701988] 2 [457:9400:1]
8400bo (1 curve)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7-  2 -7  7 -8
Curve Equation t Generators 8400bo1 [0,-1,0,-100728,12346992] 1 [-292:4096:1]
8400bp (6 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -4  2 -2  4
Curve Equation t Generators 8400bp1 [0,-1,0,3992,134512] 2 [-3:350:1] 8400bp2 [0,-1,0,-28008,1414512] 4 [-118:1750:1] 8400bp3 [0,-1,0,-148008,-20665488] 2 [-214:1078:1] 8400bp4 [0,-1,0,-420008,104902512] 4 [-28:10800:1] 8400bp5 [0,-1,0,-6720008,6707302512] 2 [1452:3000:1] 8400bp6 [0,-1,0,-392008,119462512] 2 [-14:11178:1]
8400bq (2 curves)	1	2- 3+ 5- 7+	2- 3+ 5- 7+  3 -4 -6  4
Curve Equation t Generators 8400bq1 [0,-1,0,-658,-6713] 1 [37:135:1] 8400bq2 [0,-1,0,3842,-4013] 1 [13:219:1]
8400br (2 curves)	1	2- 3+ 5- 7+	2- 3+ 5- 7+ -6 -1  3  4
Curve Equation t Generators 8400br1 [0,-1,0,392,112] 1 [12:80:1] 8400br2 [0,-1,0,-5608,172912] 1 [36:128:1]
8400bs (1 curve)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  1 -2  8  2
Curve Equation t 8400bs1 [0,-1,0,-100458,-12261213] 1
8400bt (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  2 -2 -8  2
Curve Equation t 8400bt1 [0,-1,0,-2728,-53648] 2 8400bt2 [0,-1,0,-1128,-117648] 2
8400bu (1 curve)	0	2- 3+ 5- 7-	2- 3+ 5- 7- -2  1 -1 -4
Curve Equation t 8400bu1 [0,-1,0,-12208,622912] 1
8400bv (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7- -2  6  4  6
Curve Equation t 8400bv1 [0,-1,0,-32208,-257088] 2 8400bv2 [0,-1,0,127792,-2177088] 2
8400bw (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  4  6 -2 -6
Curve Equation t 8400bw1 [0,-1,0,-3073,110092] 2 8400bw2 [0,-1,0,-57748,5358892] 2
8400bx (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7- -4 -2 -2  2
Curve Equation t 8400bx1 [0,-1,0,167,1912] 2 8400bx2 [0,-1,0,-1708,24412] 2
8400by (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  6 -2  4  6
Curve Equation t 8400by1 [0,-1,0,-288,-1728] 2 8400by2 [0,-1,0,112,-6528] 2
8400bz (1 curve)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  1  2 -8  2
Curve Equation t Generators 8400bz1 [0,1,0,-4018,-99697] 1 [119:1059:1]
8400ca (1 curve)	1	2- 3- 5+ 7+	2- 3- 5+ 7+ -2 -1  1 -4
Curve Equation t Generators 8400ca1 [0,1,0,-488,4788] 1 [22:-72:1]
8400cb (2 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+ -2 -4 -2  2
Curve Equation t Generators 8400cb1 [0,1,0,-133,-262] 2 [-294:100:27] 8400cb2 [0,1,0,492,-1512] 2 [23:150:1]
8400cc (8 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  4  2 -2 -4
Curve Equation t Generators 8400cc1 [0,1,0,83992,-7032012] 2 [103:1650:1] 8400cc2 [0,1,0,-428008,-63352012] 4 [-532:3750:1] 8400cc3 [0,1,0,-6028008,-5696952012] 2 [-1428:1062:1] 8400cc4 [0,1,0,-3020008,1973959988] 4 [-1522:55200:1] 8400cc5 [0,1,0,-48020008,128063959988] 4 [17228:2101050:1] 8400cc6 [0,1,0,507992,6313399988] 2 [-1228:61962:1] 8400cc7 [0,1,0,-768320008,8196864559988] 2 [431346:161000:27] 8400cc8 [0,1,0,-47720008,129743359988] 2 [-677338561364:141312601501806:296740963]
8400cd (6 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+ -4  2  6 -4
Curve Equation t Generators 8400cd1 [0,1,0,392,788] 2 [14:96:1] 8400cd2 [0,1,0,-1608,4788] 4 [-18:168:1] 8400cd3 [0,1,0,-15608,-751212] 2 [-68:18:1] 8400cd4 [0,1,0,-19608,1048788] 4 [38:600:1] 8400cd5 [0,1,0,-313608,67492788] 2 [332:282:1] 8400cd6 [0,1,0,-13608,1708788] 2 [68:1050:1]
8400ce (8 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  0 -2  6  4
Curve Equation t 8400ce1 [0,1,0,-16408,279188] 2 8400ce2 [0,1,0,-144408,-20968812] 4 8400ce3 [0,1,0,-1072408,427095188] 2 8400ce4 [0,1,0,-2304408,-1347208812] 2 8400ce5 [0,1,0,-32408,-52552812] 2 8400ce6 [0,1,0,-1080408,420391188] 4 8400ce7 [0,1,0,-2580408,-1004608812] 2 8400ce8 [0,1,0,291592,1416463188] 2
8400cf (8 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  0 -2  6 -8
Curve Equation t 8400cf1 [0,1,0,-199008,-34224012] 2 8400cf2 [0,1,0,-231008,-22512012] 4 8400cf3 [0,1,0,-589008,132035988] 2 8400cf4 [0,1,0,-1743008,869567988] 2 8400cf5 [0,1,0,768992,-164512012] 4 8400cf6 [0,1,0,-8781008,10011587988] 4 8400cf7 [0,1,0,-140493008,640912067988] 2 8400cf8 [0,1,0,-8141008,11533507988] 4
8400cg (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  0  6 -2  8
Curve Equation t 8400cg1 [0,1,0,-1008,-12012] 2 8400cg2 [0,1,0,-3008,47988] 4 8400cg3 [0,1,0,-45008,3659988] 2 8400cg4 [0,1,0,6992,307988] 4
8400ch (2 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  3  4  6  4
Curve Equation t 8400ch1 [0,1,0,-16458,-872037] 1 8400ch2 [0,1,0,96042,-309537] 1
8400ci (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  6 -2  0  4
Curve Equation t 8400ci1 [0,1,0,167,338] 2 8400ci2 [0,1,0,-708,2088] 2 8400ci3 [0,1,0,-2833,58838] 2 8400ci4 [0,1,0,-45708,3746088] 2
8400cj (2 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -6  1 -3  4
Curve Equation t 8400cj1 [0,1,0,9792,33588] 1 8400cj2 [0,1,0,-140208,21333588] 1
8400ck (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -6  4 -6 -2
Curve Equation t 8400ck1 [0,1,0,-1533,-23562] 2 8400ck2 [0,1,0,-908,-42312] 2 8400ck3 [0,1,0,-7533,229938] 2 8400ck4 [0,1,0,8092,1073688] 2
8400cl (1 curve)	0	2- 3- 5- 7+	2- 3- 5- 7+ -1  4  2  4
Curve Equation t 8400cl1 [0,1,0,42,963] 1
8400cm (2 curves)	0	2- 3- 5- 7+	2- 3- 5- 7+  2  2  8  2
Curve Equation t 8400cm1 [0,1,0,-68208,-6842412] 2 8400cm2 [0,1,0,-28208,-14762412] 2
8400cn (1 curve)	0	2- 3- 5- 7+	2- 3- 5- 7+  2  7 -7 -8
Curve Equation t 8400cn1 [0,1,0,-2518208,1538337588] 1
8400co (2 curves)	0	2- 3- 5- 7+	2- 3- 5- 7+ -2 -6 -4  6
Curve Equation t 8400co1 [0,1,0,-1288,-2572] 2 8400co2 [0,1,0,5112,-15372] 2
8400cp (2 curves)	0	2- 3- 5- 7+	2- 3- 5- 7+  4 -6  2 -6
Curve Equation t 8400cp1 [0,1,0,-76833,13607838] 2 8400cp2 [0,1,0,-1443708,666974088] 2
8400cq (2 curves)	0	2- 3- 5- 7+	2- 3- 5- 7+ -4  2  2  2
Curve Equation t 8400cq1 [0,1,0,7,18] 2 8400cq2 [0,1,0,-68,168] 2
8400cr (2 curves)	0	2- 3- 5- 7+	2- 3- 5- 7+  6  2 -4  6
Curve Equation t 8400cr1 [0,1,0,-7208,-230412] 2 8400cr2 [0,1,0,2792,-810412] 2
8400cs (1 curve)	1	2- 3- 5- 7-	2- 3- 5- 7-  1 -2  0 -6
Curve Equation t Generators 8400cs1 [0,1,0,42,63] 1 [3:15:1]
8400ct (2 curves)	1	2- 3- 5- 7-	2- 3- 5- 7- -2  1 -3  0
Curve Equation t Generators 8400ct1 [0,1,0,-70008,7106388] 1 [158:120:1] 8400ct2 [0,1,0,8792,22001588] 1 [1358:-50400:1]

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