Cremona's table of elliptic curves

17325 = 3² · 5² · 7 · 11

Class	r	Atkin-Lehner	Eigenvalues
17325a (2 curves)	1	3+ 5+ 7+ 11+	1 3+ 5+ 7+ 11+  2 -2  4
Curve Equation t Generators 17325a1 [1,-1,0,1896708,523398491] 2 [1925279470860838:104341786068411729:1161267062831] 17325a2 [1,-1,0,-8650167,4457382866] 2 [736503113002:59780765675824:95443993]
17325b (2 curves)	0	3+ 5+ 7+ 11-	-1 3+ 5+ 7+ 11-  2  2  4
Curve Equation t 17325b1 [1,-1,1,210745,-19455378] 2 17325b2 [1,-1,1,-961130,-164767878] 2
17325c (2 curves)	2	3+ 5+ 7- 11+	-1 3+ 5+ 7- 11+ -6 -6 -4
Curve Equation t Generators 17325c1 [1,-1,1,-5,1372] 2 [-10:23:1]&[4:35:1] 17325c2 [1,-1,1,-1880,31372] 2 [-46:160:1]&[-11:230:1]
17325d (2 curves)	1	3+ 5+ 7- 11-	1 3+ 5+ 7- 11- -6  6 -4
Curve Equation t Generators 17325d1 [1,-1,0,-42,-37009] 2 [2370:20243:27] 17325d2 [1,-1,0,-16917,-830134] 2 [358:6058:1]
17325e (1 curve)	0	3+ 5- 7+ 11+	2 3+ 5- 7+ 11+  4 -5  3
Curve Equation t 17325e1 [0,0,1,-405,7931] 1
17325f (1 curve)	1	3+ 5- 7+ 11-	-2 3+ 5- 7+ 11-  4  5  3
Curve Equation t Generators 17325f1 [0,0,1,-45,-294] 1 [20:82:1]
17325g (1 curve)	1	3+ 5- 7- 11+	-2 3+ 5- 7- 11+ -4  5  3
Curve Equation t Generators 17325g1 [0,0,1,-10125,991406] 1 [150:1687:1]
17325h (1 curve)	0	3+ 5- 7- 11-	2 3+ 5- 7- 11- -4 -5  3
Curve Equation t 17325h1 [0,0,1,-1125,-36719] 1
17325i (1 curve)	0	3- 5+ 7+ 11+	0 3- 5+ 7+ 11+  0  3 -3
Curve Equation t 17325i1 [0,0,1,-29550,-6319719] 1
17325j (1 curve)	0	3- 5+ 7+ 11+	-2 3- 5+ 7+ 11+ -3 -1  7
Curve Equation t 17325j1 [0,0,1,-69375,6085156] 1
17325k (2 curves)	0	3- 5+ 7+ 11+	-2 3- 5+ 7+ 11+  6 -7 -5
Curve Equation t 17325k1 [0,0,1,-2011575,-1285997594] 1 17325k2 [0,0,1,-6027825,107691166156] 1
17325l (2 curves)	1	3- 5+ 7+ 11-	0 3- 5+ 7+ 11-  1  3 -1
Curve Equation t Generators 17325l1 [0,0,1,-7500,-17969] 1 [-29:418:1] 17325l2 [0,0,1,-401250,97828906] 1 [364:49:1]
17325m (2 curves)	1	3- 5+ 7+ 11-	0 3- 5+ 7+ 11-  4  3 -1
Curve Equation t Generators 17325m1 [0,0,1,-300,115906] 1 [10:337:1] 17325m2 [0,0,1,-189300,31702531] 1 [-35:6187:1]
17325n (3 curves)	1	3- 5+ 7+ 11-	0 3- 5+ 7+ 11-  4 -6  2
Curve Equation t Generators 17325n1 [0,0,1,-20100,-1096844] 1 [397314:8923204:729] 17325n2 [0,0,1,-11100,-2081219] 1 [4863:35830:27] 17325n3 [0,0,1,99150,53870656] 1 [1346:51243:1]
17325o (2 curves)	1	3- 5+ 7+ 11-	0 3- 5+ 7+ 11- -5  3  5
Curve Equation t Generators 17325o1 [0,0,1,-390,-2534] 1 [-14:13:1] 17325o2 [0,0,1,-8490,300811] 1 [49:49:1]
17325p (4 curves)	1	3- 5+ 7+ 11-	1 3- 5+ 7+ 11-  2  6  4
Curve Equation t Generators 17325p1 [1,-1,0,-45792,-3757509] 2 [-275990:196643:2197] 17325p2 [1,-1,0,-55917,-1965384] 4 [-212:678:1] 17325p3 [1,-1,0,-477792,125862741] 2 [-780:5241:1] 17325p4 [1,-1,0,203958,-15219009] 2 [5332:95367:64]
17325q (4 curves)	1	3- 5+ 7+ 11-	1 3- 5+ 7+ 11-  2 -6  4
Curve Equation t Generators 17325q1 [1,-1,0,-3654567,2689983216] 2 [12462:216519:8] 17325q2 [1,-1,0,-3655692,2688245091] 4 [45076:1353837:64] 17325q3 [1,-1,0,-4658067,1097475966] 2 [1902020:13812739:8000] 17325q4 [1,-1,0,-2671317,4167760716] 2 [4824:319338:1]
17325r (4 curves)	1	3- 5+ 7+ 11-	1 3- 5+ 7+ 11- -6  2  4
Curve Equation t Generators 17325r1 [1,-1,0,-710442,-15571409] 2 [914:9443:1] 17325r2 [1,-1,0,-8091567,-8836015784] 4 [204142:32295679:8] 17325r3 [1,-1,0,-129378942,-566394078659] 2 [-2064790284:1013443363:314432] 17325r4 [1,-1,0,-4902192,-15874966409] 2 [5174:309263:1]
17325s (6 curves)	1	3- 5+ 7+ 11-	-1 3- 5+ 7+ 11-  2  2  4
Curve Equation t Generators 17325s1 [1,-1,1,7870,78064872] 2 [46172:3074205:343] 17325s2 [1,-1,1,-2693255,1671728622] 4 [-76:43350:1] 17325s3 [1,-1,1,-5725130,-2779063878] 2 [-615:22868:1] 17325s4 [1,-1,1,-42879380,108084587622] 4 [2064:167405:1] 17325s5 [1,-1,1,-686070005,6916900543872] 2 [15429:57735:1] 17325s6 [1,-1,1,-42666755,109209373872] 2 [-2566:450495:1]
17325t (2 curves)	1	3- 5+ 7+ 11-	-1 3- 5+ 7+ 11- -4 -4 -8
Curve Equation t Generators 17325t1 [1,-1,1,-5,-23628] 2 [54:335:1] 17325t2 [1,-1,1,-12380,-518628] 2 [-66:120:1]
17325u (6 curves)	1	3- 5+ 7+ 11-	-1 3- 5+ 7+ 11- -6  2  4
Curve Equation t Generators 17325u1 [1,-1,1,-7655,-255778] 2 [-50:33:1] 17325u2 [1,-1,1,-8780,-174778] 4 [-66:370:1] 17325u3 [1,-1,1,-63905,6109472] 4 [-60:3148:1] 17325u4 [1,-1,1,28345,-1288528] 2 [99:1525:1] 17325u5 [1,-1,1,-1016780,394882472] 2 [589:-20:1] 17325u6 [1,-1,1,6970,18866972] 2 [15:4348:1]
17325v (1 curve)	1	3- 5+ 7+ 11-	-2 3- 5+ 7+ 11-  2 -3  1
Curve Equation t Generators 17325v1 [0,0,1,-75,-27594] 1 [35:112:1]
17325w (4 curves)	1	3- 5+ 7- 11+	1 3- 5+ 7- 11+  2 -2 -4
Curve Equation t Generators 17325w1 [1,-1,0,-792,62491] 2 [18:223:1] 17325w2 [1,-1,0,-28917,1890616] 4 [24:1088:1] 17325w3 [1,-1,0,-45792,-556259] 2 [-76:1613:1] 17325w4 [1,-1,0,-462042,120999991] 2 [3342:5279:8]
17325x (2 curves)	1	3- 5+ 7- 11+	1 3- 5+ 7- 11+ -4  4  0
Curve Equation t Generators 17325x1 [1,-1,0,783,-32184] 2 [124:1338:1] 17325x2 [1,-1,0,-11592,-440559] 2 [-56:203:1]
17325y (6 curves)	1	3- 5+ 7- 11+	-1 3- 5+ 7- 11+  2 -6 -4
Curve Equation t Generators 17325y1 [1,-1,1,-59630,-5589628] 2 [300:1708:1] 17325y2 [1,-1,1,-60755,-5366878] 4 [-146:685:1] 17325y3 [1,-1,1,-196880,27303122] 4 [-366:7270:1] 17325y4 [1,-1,1,57370,-23794378] 2 [529:12160:1] 17325y5 [1,-1,1,-2981255,1981934372] 2 [574:21150:1] 17325y6 [1,-1,1,409495,161918372] 2 [-135:10273:1]
17325z (4 curves)	1	3- 5+ 7- 11+	-1 3- 5+ 7- 11+  6  6 -4
Curve Equation t Generators 17325z1 [1,-1,1,-8255,-386378] 2 [15618:362515:27] 17325z2 [1,-1,1,-144380,-21077378] 4 [670:13178:1] 17325z3 [1,-1,1,-2310005,-1350771128] 2 [2545:94901:1] 17325z4 [1,-1,1,-156755,-17241128] 2 [-266:2495:1]
17325ba (2 curves)	1	3- 5+ 7- 11+	2 3- 5+ 7- 11+ -1 -3  5
Curve Equation t Generators 17325ba1 [0,0,1,-607935,-78046749] 1 [-4862:65453:8] 17325ba2 [0,0,1,-195695625,1053706813281] 1 [96568116903841066:8362060511260874225:19064120082344]
17325bb (1 curve)	1	3- 5+ 7- 11+	2 3- 5+ 7- 11+  3 -3 -7
Curve Equation t Generators 17325bb1 [0,0,1,-45,101] 1 [18:23:8]
17325bc (1 curve)	1	3- 5+ 7- 11+	-2 3- 5+ 7- 11+  2  1 -7
Curve Equation t Generators 17325bc1 [0,0,1,-28425,-1850594] 1 [265:3037:1]
17325bd (1 curve)	0	3- 5+ 7- 11-	0 3- 5+ 7- 11-  1  1  7
Curve Equation t 17325bd1 [0,0,1,-77340000,261773953906] 1
17325be (1 curve)	0	3- 5+ 7- 11-	0 3- 5+ 7- 11-  4  2 -6
Curve Equation t 17325be1 [0,0,1,450,-844] 1
17325bf (1 curve)	0	3- 5+ 7- 11-	0 3- 5+ 7- 11-  4 -5  1
Curve Equation t 17325bf1 [0,0,1,122550,-8615219] 1
17325bg (4 curves)	0	3- 5+ 7- 11-	-1 3- 5+ 7- 11-  2  6  4
Curve Equation t 17325bg1 [1,-1,1,-2480,38522] 2 17325bg2 [1,-1,1,-12605,-508228] 4 17325bg3 [1,-1,1,-198230,-33920728] 2 17325bg4 [1,-1,1,11020,-2209228] 2
17325bh (1 curve)	0	3- 5+ 7- 11-	2 3- 5+ 7- 11-  2 -3 -5
Curve Equation t 17325bh1 [0,0,1,1866075,-970264719] 1
17325bi (2 curves)	1	3- 5- 7+ 11+	1 3- 5- 7+ 11+ -2  2  0
Curve Equation t Generators 17325bi1 [1,-1,0,513,-25704] 2 [6036:56157:64] 17325bi2 [1,-1,0,-10512,-389529] 2 [234:3033:1]
17325bj (2 curves)	1	3- 5- 7+ 11+	-1 3- 5- 7+ 11+  0 -6  0
Curve Equation t Generators 17325bj1 [1,-1,1,-11930,-254928] 2 [200:2208:1] 17325bj2 [1,-1,1,-163805,-25466178] 2 [-232:210:1]
17325bk (2 curves)	1	3- 5- 7+ 11+	-1 3- 5- 7+ 11+ -6  6  0
Curve Equation t Generators 17325bk1 [1,-1,1,-725,8052] 2 [14:15:1] 17325bk2 [1,-1,1,-11750,493152] 2 [60:8:1]
17325bl (2 curves)	1	3- 5- 7+ 11+	-2 3- 5- 7+ 11+  1  3  5
Curve Equation t Generators 17325bl1 [0,0,1,-7827825,8429654506] 1 [1615:22:1] 17325bl2 [0,0,1,-15198375,-9755843594] 1 [-3500:23737:1]
17325bm (1 curve)	1	3- 5- 7+ 11+	-2 3- 5- 7+ 11+ -3  3 -7
Curve Equation t Generators 17325bm1 [0,0,1,-1125,12656] 1 [0:112:1]
17325bn (1 curve)	0	3- 5- 7+ 11-	0 3- 5- 7+ 11- -1 -1  7
Curve Equation t 17325bn1 [0,0,1,-3093600,2094191631] 1
17325bo (2 curves)	0	3- 5- 7+ 11-	1 3- 5- 7+ 11-  4  2  0
Curve Equation t 17325bo1 [1,-1,0,-228492,41829291] 2 17325bo2 [1,-1,0,-380367,-20591334] 2
17325bp (2 curves)	0	3- 5- 7- 11+	1 3- 5- 7- 11+  0  6  0
Curve Equation t 17325bp1 [1,-1,0,-477,-1944] 2 17325bp2 [1,-1,0,-6552,-202419] 2
17325bq (2 curves)	0	3- 5- 7- 11+	1 3- 5- 7- 11+  6 -6  0
Curve Equation t 17325bq1 [1,-1,0,-18117,988416] 2 17325bq2 [1,-1,0,-293742,61350291] 2
17325br (2 curves)	0	3- 5- 7- 11+	-1 3- 5- 7- 11+  2 -2  0
Curve Equation t 17325br1 [1,-1,1,12820,-3200178] 2 17325br2 [1,-1,1,-262805,-48953928] 2
17325bs (1 curve)	0	3- 5- 7- 11+	2 3- 5- 7- 11+  3  1  7
Curve Equation t 17325bs1 [0,0,1,-2775,48681] 1
17325bt (2 curves)	1	3- 5- 7- 11-	0 3- 5- 7- 11- -1 -3 -1
Curve Equation t Generators 17325bt1 [0,0,1,-300,-144] 1 [-4:31:1] 17325bt2 [0,0,1,-16050,782631] 3 [-145:247:1]
17325bu (2 curves)	1	3- 5- 7- 11-	0 3- 5- 7- 11-  5 -3  5
Curve Equation t Generators 17325bu1 [0,0,1,-9750,-316719] 1 [-398:1697:8] 17325bu2 [0,0,1,-212250,37601406] 3 [-250:8662:1]
17325bv (2 curves)	1	3- 5- 7- 11-	-1 3- 5- 7- 11- -4 -2  0
Curve Equation t Generators 17325bv1 [1,-1,1,-9140,336462] 2 [74:210:1] 17325bv2 [1,-1,1,-15215,-161688] 2 [-76:780:1]

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

Part of Computational Number Theory
Back to Tables and computations