Cremona's table of elliptic curves

86190 = 2 · 3 · 5 · 13² · 17

Class	r	Atkin-Lehner	Eigenvalues
86190a (2 curves)	1	2+ 3+ 5+ 13+ 17+	2+ 3+ 5+  2  0 13+ 17+ -2
Curve Equation t Generators 86190a1 [1,1,0,-2301783,1327857237] 2 [542:15217:1] 86190a2 [1,1,0,-354903,3504858453] 2 [-879:56463:1]
86190b (1 curve)	1	2+ 3+ 5+ 13+ 17+	2+ 3+ 5+ -3 -1 13+ 17+ -4
Curve Equation t Generators 86190b1 [1,1,0,-122528,16139232] 1 [239:641:1]
86190c (4 curves)	1	2+ 3+ 5+ 13+ 17+	2+ 3+ 5+ -4  4 13+ 17+ -8
Curve Equation t Generators 86190c1 [1,1,0,267017,9116437] 2 [291:10417:1] 86190c2 [1,1,0,-1084983,72119637] 4 [6:8097:1] 86190c3 [1,1,0,-10853183,-13695181443] 2 [-243455:-843833:125] 86190c4 [1,1,0,-12948783,17898665517] 2 [2203:7276:1]
86190d (8 curves)	2	2+ 3+ 5+ 13+ 17-	2+ 3+ 5+  0 -4 13+ 17- -4
Curve Equation t Generators 86190d1 [1,1,0,-13523,738093] 2 [-89:1161:1]&[31:576:1] 86190d2 [1,1,0,-229843,42314797] 4 [-359:9052:1]&[-122:8341:1] 86190d3 [1,1,0,-243363,37039293] 4 [-502:5997:1]&[-451:7663:1] 86190d4 [1,1,0,-3677443,2712825757] 2 [1107:-539:1]&[3177:150427:1] 86190d5 [1,1,0,517137,223057593] 2 [-346:1863:1]&[369:-21732:1] 86190d6 [1,1,0,-1220183,-486340863] 4 [-723:4671:1]&[-583:5516:1] 86190d7 [1,1,0,1106947,-2119520697] 2 [1383:44685:1]&[5163:373260:1] 86190d8 [1,1,0,-19176433,-32329954613] 2 [12229:1243756:1]&[-200776331:121340719:79507]
86190e (1 curve)	0	2+ 3+ 5+ 13+ 17-	2+ 3+ 5+  2 -1 13+ 17- -4
Curve Equation t 86190e1 [1,1,0,-1034623918,-12812103048428] 1
86190f (1 curve)	0	2+ 3+ 5+ 13+ 17-	2+ 3+ 5+  3  5 13+ 17-  2
Curve Equation t 86190f1 [1,1,0,-18093988,-8060278832] 1
86190g (4 curves)	0	2+ 3+ 5+ 13+ 17-	2+ 3+ 5+  4  4 13+ 17- -8
Curve Equation t 86190g1 [1,1,0,-545873,85325973] 2 86190g2 [1,1,0,-4006993,-3028989803] 4 86190g3 [1,1,0,373487,-9292200107] 2 86190g4 [1,1,0,-63765393,-196012766763] 2
86190h (1 curve)	0	2+ 3+ 5+ 13+ 17-	2+ 3+ 5+  4 -5 13+ 17-  7
Curve Equation t 86190h1 [1,1,0,-238293,44725413] 1
86190i (4 curves)	0	2+ 3+ 5+ 13+ 17-	2+ 3+ 5+ -4 -4 13+ 17- -4
Curve Equation t 86190i1 [1,1,0,158012,19086592] 2 86190i2 [1,1,0,-818808,171275148] 4 86190i3 [1,1,0,-5674178,-5081264118] 2 86190i4 [1,1,0,-11592558,15183418398] 2
86190j (2 curves)	2	2+ 3+ 5+ 13- 17+	2+ 3+ 5+  0  0 13- 17+ -2
Curve Equation t Generators 86190j1 [1,1,0,-198,-1152] 2 [-9:6:1]&[-66:51:8] 86190j2 [1,1,0,-68,-2478] 2 [17:32:1]&[19:50:1]
86190k (2 curves)	0	2+ 3+ 5+ 13- 17+	2+ 3+ 5+  4  4 13- 17+  2
Curve Equation t 86190k1 [1,1,0,-781628,250778832] 2 86190k2 [1,1,0,624452,1055337808] 2
86190l (2 curves)	1	2+ 3+ 5+ 13- 17-	2+ 3+ 5+  2  4 13- 17-  0
Curve Equation t Generators 86190l1 [1,1,0,-56618,3985428] 2 [821:22211:1] 86190l2 [1,1,0,-847538,299947692] 2 [539:11:1]
86190m (1 curve)	0	2+ 3+ 5- 13+ 17+	2+ 3+ 5-  2 -5 13+ 17+  6
Curve Equation t 86190m1 [1,1,0,59823,-54061509] 1
86190n (2 curves)	0	2+ 3+ 5- 13+ 17+	2+ 3+ 5- -2  0 13+ 17+ -4
Curve Equation t 86190n1 [1,1,0,2363,118201] 2 86190n2 [1,1,0,-26367,1457019] 2
86190o (1 curve)	1	2+ 3+ 5- 13+ 17-	2+ 3+ 5- -1  5 13+ 17- -1
Curve Equation t Generators 86190o1 [1,1,0,-17072,-11121144] 1 [2267:106604:1]
86190p (1 curve)	1	2+ 3+ 5- 13+ 17-	2+ 3+ 5-  2 -1 13+ 17-  2
Curve Equation t Generators 86190p1 [1,1,0,8588018,-18680853836] 1 [75441:4410202:27]
86190q (1 curve)	1	2+ 3+ 5- 13+ 17-	2+ 3+ 5- -2  1 13+ 17-  1
Curve Equation t Generators 86190q1 [1,1,0,-703212,564680784] 1 [395:18477:1]
86190r (4 curves)	1	2+ 3+ 5- 13+ 17-	2+ 3+ 5-  4  4 13+ 17-  4
Curve Equation t Generators 86190r1 [1,1,0,-17072,742656] 2 [-73:1304:1] 86190r2 [1,1,0,-71152,-6579776] 4 [-137:856:1] 86190r3 [1,1,0,97848,-32909976] 2 [1215:42768:1] 86190r4 [1,1,0,-1105432,-447803624] 2 [1461:31802:1]
86190s (2 curves)	1	2+ 3+ 5- 13- 17+	2+ 3+ 5-  0  2 13- 17+  2
Curve Equation t Generators 86190s1 [1,1,0,-3487,-80699] 2 [-35:19:1] 86190s2 [1,1,0,-2967,-104931] 2 [69:123:1]
86190t (2 curves)	1	2+ 3+ 5- 13- 17+	2+ 3+ 5- -2  4 13- 17+ -4
Curve Equation t Generators 86190t1 [1,1,0,-1277,-5559] 2 [-8:69:1] 86190t2 [1,1,0,-11807,485139] 2 [83:-334:1]
86190u (1 curve)	0	2+ 3- 5+ 13+ 17+	2+ 3- 5+  1  0 13+ 17+  0
Curve Equation t 86190u1 [1,0,1,-69,496] 1
86190v (1 curve)	0	2+ 3- 5+ 13+ 17+	2+ 3- 5+  2  3 13+ 17+  7
Curve Equation t 86190v1 [1,0,1,3035236,5192852186] 1
86190w (4 curves)	0	2+ 3- 5+ 13+ 17+	2+ 3- 5+ -2  0 13+ 17+  4
Curve Equation t 86190w1 [1,0,1,4221,-828098] 2 86190w2 [1,0,1,-110699,-13561234] 2 86190w3 [1,0,1,-553479,-158586218] 2 86190w4 [1,0,1,-8856449,-10145398534] 2
86190x (2 curves)	0	2+ 3- 5+ 13+ 17+	2+ 3- 5+ -2  0 13+ 17+ -6
Curve Equation t 86190x1 [1,0,1,-111109054,450778669616] 2 86190x2 [1,0,1,-110987374,451815285872] 2
86190y (2 curves)	0	2+ 3- 5+ 13+ 17+	2+ 3- 5+  4  3 13+ 17+  1
Curve Equation t 86190y1 [1,0,1,-3666459,2710425382] 1 86190y2 [1,0,1,8095941,14171221222] 1
86190z (4 curves)	1	2+ 3- 5+ 13+ 17-	2+ 3- 5+  0  0 13+ 17- -4
Curve Equation t Generators 86190z1 [1,0,1,-51549,-877784] 2 [248:1143:1] 86190z2 [1,0,1,-622769,-188923408] 4 [-466:615:1] 86190z3 [1,0,1,-425039,-310962364] 2 [139480:3003279:125] 86190z4 [1,0,1,-9960019,-12099519508] 2 [1158230:103340866:125]
86190ba (1 curve)	1	2+ 3- 5+ 13+ 17-	2+ 3- 5+  1  1 13+ 17-  2
Curve Equation t Generators 86190ba1 [1,0,1,-25311134,48870359696] 1 [1506:118276:1]
86190bb (1 curve)	1	2+ 3- 5+ 13+ 17-	2+ 3- 5+  4 -3 13+ 17-  6
Curve Equation t Generators 86190bb1 [1,0,1,-474049,143333972] 1 [-662:13259:1]
86190bc (2 curves)	1	2+ 3- 5+ 13- 17+	2+ 3- 5+ -2 -4 13- 17+  2
Curve Equation t Generators 86190bc1 [1,0,1,64216,-174945418] 2 [921:25339:1] 86190bc2 [1,0,1,-4329784,-3380807818] 2 [-1259:9299:1]
86190bd (2 curves)	1	2+ 3- 5- 13+ 17+	2+ 3- 5-  1  3 13+ 17+ -2
Curve Equation t Generators 86190bd1 [1,0,1,-1083,-6914] 1 [-28:54:1] 86190bd2 [1,0,1,-74793,-7879142] 1 [-158:80:1]
86190be (2 curves)	1	2+ 3- 5- 13+ 17+	2+ 3- 5- -1 -3 13+ 17+ -1
Curve Equation t Generators 86190be1 [1,0,1,-1467093,-29088656192] 3 [4004:168975:1] 86190be2 [1,0,1,-762233268,-8100305256782] 1 [96485896:41359429701:512]
86190bf (1 curve)	1	2+ 3- 5- 13+ 17+	2+ 3- 5-  2  1 13+ 17+ -1
Curve Equation t Generators 86190bf1 [1,0,1,-40733,3294488] 1 [222:2170:1]
86190bg (2 curves)	1	2+ 3- 5- 13+ 17+	2+ 3- 5- -2 -3 13+ 17+  4
Curve Equation t Generators 86190bg1 [1,0,1,347,9128] 1 [-8:80:1] 86190bg2 [1,0,1,-3163,-261844] 1 [382:7178:1]
86190bh (1 curve)	1	2+ 3- 5- 13+ 17+	2+ 3- 5- -4  1 13+ 17+  8
Curve Equation t Generators 86190bh1 [1,0,1,22,-13102] 1 [54:-410:1]
86190bi (4 curves)	0	2+ 3- 5- 13+ 17-	2+ 3- 5-  0 -4 13+ 17-  4
Curve Equation t 86190bi1 [1,0,1,672,-674] 2 86190bi2 [1,0,1,-2708,-6082] 4 86190bi3 [1,0,1,-28058,1798838] 2 86190bi4 [1,0,1,-31438,-2143594] 2
86190bj (1 curve)	0	2+ 3- 5- 13+ 17-	2+ 3- 5-  1  4 13+ 17- -4
Curve Equation t 86190bj1 [1,0,1,-28058,-2287582] 1
86190bk (1 curve)	0	2+ 3- 5- 13+ 17-	2+ 3- 5- -2 -3 13+ 17-  0
Curve Equation t 86190bk1 [1,0,1,-7607708,-8078898982] 1
86190bl (1 curve)	0	2+ 3- 5- 13+ 17-	2+ 3- 5-  3 -5 13+ 17- -7
Curve Equation t 86190bl1 [1,0,1,-214803,-46284704] 1
86190bm (8 curves)	0	2+ 3- 5- 13+ 17-	2+ 3- 5-  4  0 13+ 17-  4
Curve Equation t 86190bm1 [1,0,1,-354248678,2471124782648] 2 86190bm2 [1,0,1,-939177958,-7792278335944] 4 86190bm3 [1,0,1,-4358980838,-110049775142344] 2 86190bm4 [1,0,1,2514857562,-51791164403912] 4 86190bm5 [1,0,1,-13752081958,-620648852140744] 2 86190bm6 [1,0,1,-69617438518,-7070099217161992] 4 86190bm7 [1,0,1,-69491198898,-7097017240838744] 4 86190bm8 [1,0,1,-1113879001018,-452486084448911992] 2
86190bn (1 curve)	0	2+ 3- 5- 13+ 17-	2+ 3- 5-  4  1 13+ 17- -4
Curve Equation t 86190bn1 [1,0,1,672,121006] 1
86190bo (2 curves)	0	2- 3+ 5+ 13+ 17+	2- 3+ 5+  0 -2 13+ 17+  4
Curve Equation t 86190bo1 [1,1,1,-75659191,-253333397491] 2 86190bo2 [1,1,1,-74253111,-263200142067] 2
86190bp (1 curve)	0	2- 3+ 5+ 13+ 17+	2- 3+ 5+  0  3 13+ 17+ -1
Curve Equation t 86190bp1 [1,1,1,-2961,126693] 1
86190bq (1 curve)	0	2- 3+ 5+ 13+ 17+	2- 3+ 5+  2 -5 13+ 17+  1
Curve Equation t 86190bq1 [1,1,1,645999,-87285177] 1
86190br (1 curve)	0	2- 3+ 5+ 13+ 17+	2- 3+ 5+ -2  5 13+ 17+ -6
Curve Equation t 86190br1 [1,1,1,354,-24471] 1
86190bs (4 curves)	0	2- 3+ 5+ 13+ 17+	2- 3+ 5+  4  4 13+ 17+  8
Curve Equation t 86190bs1 [1,1,1,-99291,11984409] 2 86190bs2 [1,1,1,-129711,3990033] 4 86190bs3 [1,1,1,504039,32128533] 2 86190bs4 [1,1,1,-1250181,-535180131] 2
86190bt (1 curve)	1	2- 3+ 5+ 13+ 17-	2- 3+ 5+  1 -5 13+ 17-  1
Curve Equation t Generators 86190bt1 [1,1,1,-101,-5101] 1 [21:40:1]
86190bu (1 curve)	1	2- 3+ 5+ 13+ 17-	2- 3+ 5+ -2  1 13+ 17- -2
Curve Equation t Generators 86190bu1 [1,1,1,1451374954,-41049092752621] 1 [5843129501:12240295480873:1331]
86190bv (2 curves)	1	2- 3+ 5+ 13- 17+	2- 3+ 5+  0 -2 13- 17+ -2
Curve Equation t Generators 86190bv1 [1,1,1,-589391,-174348907] 2 [-441:442:1] 86190bv2 [1,1,1,-501511,-228026011] 2 [3953:242112:1]
86190bw (2 curves)	1	2- 3+ 5+ 13- 17+	2- 3+ 5+  2 -4 13- 17+  4
Curve Equation t Generators 86190bw1 [1,1,1,-215901,-11133777] 2 [602411126872:-26912863602313:292754944] 86190bw2 [1,1,1,-1995471,1075827579] 2 [524308:46533629:64]
86190bx (1 curve)	1	2- 3+ 5- 13+ 17+	2- 3+ 5-  0 -3 13+ 17+  3
Curve Equation t Generators 86190bx1 [1,1,1,52640,674233217] 1 [1045:42741:1]
86190by (4 curves)	1	2- 3+ 5- 13+ 17+	2- 3+ 5-  0  4 13+ 17+  4
Curve Equation t Generators 86190by1 [1,1,1,-306485,-6312828085] 4 [186051:15152476:27] 86190by2 [1,1,1,-53118985,-147068703085] 4 [73154063163:2601916045438:8120601] 86190by3 [1,1,1,-104452735,183253711415] 2 [32309621138210503343322:-1031780897777331900788263:3309374508917920344] 86190by4 [1,1,1,-846785235,-9484710867585] 2 [1714787265434423244:-888465263961010583281:6323414551488]
86190bz (1 curve)	1	2- 3+ 5- 13+ 17+	2- 3+ 5- -2  1 13+ 17+  5
Curve Equation t Generators 86190bz1 [1,1,1,5320,-307975] 1 [83:-887:1]
86190ca (1 curve)	1	2- 3+ 5- 13+ 17+	2- 3+ 5-  3  1 13+ 17+  4
Curve Equation t Generators 86190ca1 [1,1,1,-725,7067] 1 [27:-104:1]
86190cb (1 curve)	0	2- 3+ 5- 13+ 17-	2- 3+ 5- -2  1 13+ 17-  4
Curve Equation t 86190cb1 [1,1,1,-6122035,-5833990063] 1
86190cc (2 curves)	0	2- 3+ 5- 13+ 17-	2- 3+ 5- -2  4 13+ 17-  4
Curve Equation t 86190cc1 [1,1,1,-451825,151208975] 2 86190cc2 [1,1,1,-7806705,8391616527] 2
86190cd (1 curve)	2	2- 3+ 5- 13+ 17-	2- 3+ 5- -3 -5 13+ 17- -2
Curve Equation t Generators 86190cd1 [1,1,1,-107065,-3709945] 1 [-307:738:1]&[-47:-1082:1]
86190ce (4 curves)	0	2- 3+ 5- 13+ 17-	2- 3+ 5-  4  4 13+ 17-  4
Curve Equation t 86190ce1 [1,1,1,-35240,2531225] 4 86190ce2 [1,1,1,-38620,2012057] 4 86190ce3 [1,1,1,105030,13618977] 2 86190ce4 [1,1,1,-236350,-42754015] 2
86190cf (2 curves)	0	2- 3+ 5- 13- 17+	2- 3+ 5-  0  0 13- 17+  2
Curve Equation t 86190cf1 [1,1,1,-33550,-2363353] 2 86190cf2 [1,1,1,-11580,-5386425] 2
86190cg (2 curves)	2	2- 3+ 5- 13- 17+	2- 3+ 5- -4 -4 13- 17+ -2
Curve Equation t Generators 86190cg1 [1,1,1,-4625,112367] 2 [-73:296:1]&[-69:364:1] 86190cg2 [1,1,1,3695,481775] 2 [43:-872:1]&[-47:478:1]
86190ch (2 curves)	1	2- 3+ 5- 13- 17-	2- 3+ 5- -2 -4 13- 17-  0
Curve Equation t Generators 86190ch1 [1,1,1,-335,1685] 2 [5:10:1] 86190ch2 [1,1,1,-5015,134597] 2 [45:-74:1]
86190ci (2 curves)	1	2- 3- 5+ 13+ 17+	2- 3- 5+  1  3 13+ 17+  1
Curve Equation t Generators 86190ci1 [1,0,0,-8681,-13240839] 1 [1120:36619:1] 86190ci2 [1,0,0,-4510256,-3687331584] 1 [2680:57616:1]
86190cj (2 curves)	1	2- 3- 5+ 13+ 17+	2- 3- 5+ -1 -3 13+ 17+  2
Curve Equation t Generators 86190cj1 [1,0,0,-182946,-15006564] 3 [-102:1662:1] 86190cj2 [1,0,0,-12639936,-17297834490] 1 [-174861060:93705375:85184]
86190ck (2 curves)	1	2- 3- 5+ 13+ 17+	2- 3- 5+  2  3 13+ 17+ -4
Curve Equation t Generators 86190ck1 [1,0,0,58724,19996040] 3 [-154:2780:1] 86190ck2 [1,0,0,-534466,-574736254] 1 [45893708:1871383121:21952]
86190cl (1 curve)	1	2- 3- 5+ 13+ 17+	2- 3- 5+  4 -1 13+ 17+ -8
Curve Equation t Generators 86190cl1 [1,0,0,3799,-28788345] 1 [3254482:8742793:10648]
86190cm (1 curve)	0	2- 3- 5+ 13+ 17-	2- 3- 5+ -1 -4 13+ 17-  4
Curve Equation t 86190cm1 [1,0,0,-166,-1054] 1
86190cn (2 curves)	0	2- 3- 5+ 13+ 17-	2- 3- 5+  2  0 13+ 17- -6
Curve Equation t 86190cn1 [1,0,0,-79011,-6384015] 2 86190cn2 [1,0,0,194769,-40825539] 2
86190co (1 curve)	0	2- 3- 5+ 13+ 17-	2- 3- 5+  2  3 13+ 17-  0
Curve Equation t 86190co1 [1,0,0,-45016,-3680704] 1
86190cp (1 curve)	0	2- 3- 5+ 13+ 17-	2- 3- 5+  2  3 13+ 17-  3
Curve Equation t 86190cp1 [1,0,0,-15388010661,734719158506241] 1
86190cq (2 curves)	0	2- 3- 5+ 13+ 17-	2- 3- 5+  2 -4 13+ 17- -4
Curve Equation t 86190cq1 [1,0,0,-122106,-16649244] 2 86190cq2 [1,0,0,-1960826,-1056997020] 2
86190cr (2 curves)	0	2- 3- 5+ 13+ 17-	2- 3- 5+ -2  3 13+ 17-  7
Curve Equation t 86190cr1 [1,0,0,-49436,-4770234] 1 86190cr2 [1,0,0,-4143461,-3246677799] 1
86190cs (1 curve)	0	2- 3- 5+ 13+ 17-	2- 3- 5+ -3  5 13+ 17-  7
Curve Equation t 86190cs1 [1,0,0,-1271,-21165] 1
86190ct (1 curve)	0	2- 3- 5+ 13+ 17-	2- 3- 5+ -4 -1 13+ 17-  4
Curve Equation t 86190ct1 [1,0,0,113649,265737081] 1
86190cu (4 curves)	0	2- 3- 5- 13+ 17+	2- 3- 5-  0  0 13+ 17+ -4
Curve Equation t 86190cu1 [1,0,0,462465,-185436135] 2 86190cu2 [1,0,0,-3444815,-1969500183] 4 86190cu3 [1,0,0,-17407595,26215767525] 2 86190cu4 [1,0,0,-51998515,-144319237843] 2
86190cv (1 curve)	0	2- 3- 5- 13+ 17+	2- 3- 5- -1  0 13+ 17+  0
Curve Equation t 86190cv1 [1,0,0,-11580,1101840] 1
86190cw (4 curves)	0	2- 3- 5- 13+ 17+	2- 3- 5- -2  0 13+ 17+ -2
Curve Equation t 86190cw1 [1,0,0,-493230,-5917068] 2 86190cw2 [1,0,0,1970790,-46819800] 2 86190cw3 [1,0,0,-28076565,-57263759775] 2 86190cw4 [1,0,0,-27589845,-59344682463] 2
86190cx (2 curves)	0	2- 3- 5- 13+ 17+	2- 3- 5-  4 -2 13+ 17+  4
Curve Equation t 86190cx1 [1,0,0,-119740,15929900] 2 86190cx2 [1,0,0,-97770,21962862] 2
86190cy (1 curve)	1	2- 3- 5- 13+ 17-	2- 3- 5- -1 -1 13+ 17- -2
Curve Equation t Generators 86190cy1 [1,0,0,-149770,22232612] 1 [-76:5798:1]
86190cz (1 curve)	1	2- 3- 5- 13+ 17-	2- 3- 5- -4  3 13+ 17- -6
Curve Equation t Generators 86190cz1 [1,0,0,-2805,65025] 1 [0:255:1]
86190da (1 curve)	1	2- 3- 5- 13+ 17-	2- 3- 5- -4  5 13+ 17-  1
Curve Equation t Generators 86190da1 [1,0,0,17724970,22142592900] 1 [17200:-2335730:1]
86190db (2 curves)	1	2- 3- 5- 13- 17+	2- 3- 5-  2  4 13- 17+ -2
Curve Equation t Generators 86190db1 [1,0,0,380,-79600] 2 [50:230:1] 86190db2 [1,0,0,-25620,-1540800] 2 [-90:240:1]

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