Cremona's table of elliptic curves

51150 = 2 · 3 · 5² · 11 · 31

Class	r	Atkin-Lehner	Eigenvalues
51150a (4 curves)	0	2+ 3+ 5+ 11+ 31-	2+ 3+ 5+  0 11+  2  6  0
Curve Equation t 51150a1 [1,1,0,2648500,-4121550000] 2 51150a2 [1,1,0,-28103500,-50649326000] 4 51150a3 [1,1,0,-113353500,412343424000] 2 51150a4 [1,1,0,-434885500,-3490804700000] 2
51150b (2 curves)	0	2+ 3+ 5+ 11+ 31-	2+ 3+ 5+  0 11+ -4  0  6
Curve Equation t 51150b1 [1,1,0,-21400,-1208000] 2 51150b2 [1,1,0,-9400,-2540000] 2
51150c (4 curves)	0	2+ 3+ 5+ 11+ 31-	2+ 3+ 5+ -2 11+ -2  0 -4
Curve Equation t 51150c1 [1,1,0,-1213525,201350125] 2 51150c2 [1,1,0,4418475,1547398125] 2 51150c3 [1,1,0,-52189525,-145134681875] 2 51150c4 [1,1,0,-49527525,-160598239875] 2
51150d (1 curve)	0	2+ 3+ 5+ 11+ 31-	2+ 3+ 5+  3 11+  2  3  0
Curve Equation t 51150d1 [1,1,0,-318125,68932125] 1
51150e (1 curve)	0	2+ 3+ 5+ 11+ 31-	2+ 3+ 5+  3 11+ -4 -1 -6
Curve Equation t 51150e1 [1,1,0,31750,4612500] 1
51150f (1 curve)	0	2+ 3+ 5+ 11- 31+	2+ 3+ 5+ -1 11- -4  5  6
Curve Equation t 51150f1 [1,1,0,-7300,-464750] 1
51150g (4 curves)	2	2+ 3+ 5+ 11- 31+	2+ 3+ 5+ -4 11- -2 -2  0
Curve Equation t Generators 51150g1 [1,1,0,400,0] 2 [16:96:1]&[49:350:1] 51150g2 [1,1,0,-1600,-2000] 4 [-35:130:1]&[-258:1183:8] 51150g3 [1,1,0,-18100,-942500] 2 [-79:86:1]&[-75:50:1] 51150g4 [1,1,0,-17100,850500] 2 [90:-270:1]&[-1130:6065:8]
51150h (1 curve)	1	2+ 3+ 5+ 11- 31-	2+ 3+ 5+ -1 11-  0 -5  3
Curve Equation t Generators 51150h1 [1,1,0,3425,-72875] 1 [26:173:1]
51150i (2 curves)	1	2+ 3+ 5+ 11- 31-	2+ 3+ 5+  2 11-  4 -2 -6
Curve Equation t Generators 51150i1 [1,1,0,-11775,475125] 2 [101:523:1] 51150i2 [1,1,0,-27275,-1059375] 2 [-100:875:1]
51150j (2 curves)	1	2+ 3+ 5+ 11- 31-	2+ 3+ 5+  2 11-  4  6 -2
Curve Equation t Generators 51150j1 [1,1,0,-1582225,761039125] 2 [801:2498:1] 51150j2 [1,1,0,-2574225,-309328875] 2 [-1390:24895:1]
51150k (4 curves)	1	2+ 3+ 5+ 11- 31-	2+ 3+ 5+  2 11-  6 -8  0
Curve Equation t Generators 51150k1 [1,1,0,-12166875,16326532125] 2 [957780670:2424213665:456533] 51150k2 [1,1,0,-10758875,20250628125] 2 [3430:152285:1] 51150k3 [1,1,0,-218296875,-1238913937875] 2 [7432670:699783715:343] 51150k4 [1,1,0,-137771375,-2164393509375] 2 [75280:20311535:1]
51150l (2 curves)	1	2+ 3+ 5+ 11- 31-	2+ 3+ 5+ -3 11-  1 -3  0
Curve Equation t Generators 51150l1 [1,1,0,-9625,653125] 1 [-25:950:1] 51150l2 [1,1,0,-193375,-78018125] 1 [725:12425:1]
51150m (1 curve)	0	2+ 3+ 5- 11+ 31+	2+ 3+ 5-  1 11+ -1 -3 -4
Curve Equation t 51150m1 [1,1,0,-825,-67875] 1
51150n (2 curves)	0	2+ 3+ 5- 11+ 31+	2+ 3+ 5-  2 11+ -6  4  4
Curve Equation t 51150n1 [1,1,0,-10325575,-12774132875] 2 51150n2 [1,1,0,-165205575,-817375732875] 2
51150o (1 curve)	0	2+ 3+ 5- 11+ 31+	2+ 3+ 5- -3 11+  4 -1 -1
Curve Equation t 51150o1 [1,1,0,-548075,231922125] 1
51150p (2 curves)	2	2+ 3+ 5- 11+ 31+	2+ 3+ 5- -4 11+  0  4 -8
Curve Equation t Generators 51150p1 [1,1,0,-95,-75] 2 [-6:21:1]&[-5:20:1] 51150p2 [1,1,0,-995,11625] 2 [-290:475:8]&[-20:165:1]
51150q (2 curves)	1	2+ 3+ 5- 11- 31+	2+ 3+ 5-  4 11- -4  0 -4
Curve Equation t Generators 51150q1 [1,1,0,-131450,16516500] 2 [385:4620:1] 51150q2 [1,1,0,-491450,-114883500] 2 [-436:4310:1]
51150r (6 curves)	0	2+ 3- 5+ 11+ 31+	2+ 3- 5+  0 11+  2 -2  4
Curve Equation t 51150r1 [1,0,1,-33601,2495348] 2 51150r2 [1,0,1,-545601,155071348] 4 51150r3 [1,0,1,-553601,150287348] 4 51150r4 [1,0,1,-8729601,9926767348] 2 51150r5 [1,0,1,407399,617333348] 2 51150r6 [1,0,1,-1642601,-622902652] 2
51150s (2 curves)	0	2+ 3- 5+ 11+ 31+	2+ 3- 5+  2 11+  0  6  6
Curve Equation t 51150s1 [1,0,1,-76876,4501898] 2 51150s2 [1,0,1,-1068876,425109898] 2
51150t (1 curve)	0	2+ 3- 5+ 11+ 31+	2+ 3- 5+  2 11+ -6 -3 -6
Curve Equation t 51150t1 [1,0,1,-82723026,-290563473692] 1
51150u (2 curves)	2	2+ 3- 5+ 11+ 31+	2+ 3- 5+ -2 11+ -4 -2 -2
Curve Equation t Generators 51150u1 [1,0,1,-2426,-25252] 2 [81:517:1]&[-27:157:1] 51150u2 [1,0,1,-17926,904748] 2 [52:311:1]&[-137:959:1]
51150v (4 curves)	0	2+ 3- 5+ 11+ 31+	2+ 3- 5+  4 11+  6 -2 -4
Curve Equation t 51150v1 [1,0,1,-301025776,2010241433198] 2 51150v2 [1,0,1,-301026276,2010234421198] 4 51150v3 [1,0,1,-295020026,2094297896198] 2 51150v4 [1,0,1,-307040526,1925722180198] 2
51150w (4 curves)	1	2+ 3- 5+ 11+ 31-	2+ 3- 5+  0 11+  2 -2  0
Curve Equation t Generators 51150w1 [1,0,1,-564526,-114043552] 2 [106020:469448:125] 51150w2 [1,0,1,-8252526,-9124379552] 4 [467862540:173925458989:3375] 51150w3 [1,0,1,-7477526,-10906879552] 2 [480605029202136660:-179145856854737277016:3466947585375] 51150w4 [1,0,1,-132035526,-583972631552] 2 [-9669767563391254099750486:4837622561719705144930612:1457553958621031998637]
51150x (1 curve)	1	2+ 3- 5+ 11- 31+	2+ 3- 5+ -1 11-  2 -3  0
Curve Equation t Generators 51150x1 [1,0,1,-3901,139448] 1 [-8:416:1]
51150y (1 curve)	1	2+ 3- 5+ 11- 31+	2+ 3- 5+  2 11-  2 -3 -6
Curve Equation t Generators 51150y1 [1,0,1,-260521,-65299792] 1 [673:7682:1]
51150z (2 curves)	0	2+ 3- 5+ 11- 31-	2+ 3- 5+  0 11- -4 -8  6
Curve Equation t 51150z1 [1,0,1,-66119776,-206771358802] 2 51150z2 [1,0,1,-50567776,-306552990802] 2
51150ba (2 curves)	1	2+ 3- 5- 11+ 31+	2+ 3- 5- -2 11+ -2  0  4
Curve Equation t Generators 51150ba1 [1,0,1,-6541,193928] 2 [28:167:1] 51150ba2 [1,0,1,-103341,12777928] 2 [182:-174:1]
51150bb (1 curve)	1	2+ 3- 5- 11+ 31+	2+ 3- 5- -5 11+  7  3  4
Curve Equation t Generators 51150bb1 [1,0,1,-5451,-291452] 1 [302:4911:1]
51150bc (2 curves)	0	2+ 3- 5- 11- 31+	2+ 3- 5- -2 11- -2  0  4
Curve Equation t 51150bc1 [1,0,1,-19497451,-33020076202] 2 51150bc2 [1,0,1,-29177451,3202483798] 2
51150bd (1 curve)	0	2+ 3- 5- 11- 31+	2+ 3- 5- -3 11- -3  7  4
Curve Equation t 51150bd1 [1,0,1,-3196,-72262] 1
51150be (2 curves)	0	2+ 3- 5- 11- 31+	2+ 3- 5-  4 11-  4  0  4
Curve Equation t 51150be1 [1,0,1,-499778221,4300410337688] 2 51150be2 [1,0,1,-499779121,4300394074688] 2
51150bf (2 curves)	1	2+ 3- 5- 11- 31-	2+ 3- 5-  0 11-  6  2 -4
Curve Equation t Generators 51150bf1 [1,0,1,-18701,-977452] 2 [-84:91:1] 51150bf2 [1,0,1,-4951,-2379952] 2 [166:1091:1]
51150bg (1 curve)	1	2+ 3- 5- 11- 31-	2+ 3- 5- -2 11- -6 -1 -2
Curve Equation t Generators 51150bg1 [1,0,1,2799,7048] 1 [77:786:1]
51150bh (4 curves)	0	2- 3+ 5+ 11+ 31+	2- 3+ 5+  0 11+  2 -2  4
Curve Equation t 51150bh1 [1,1,1,-72063,7415781] 4 51150bh2 [1,1,1,-74063,6979781] 4 51150bh3 [1,1,1,96437,34600781] 2 51150bh4 [1,1,1,-276563,-48505219] 2
51150bi (1 curve)	0	2- 3+ 5+ 11+ 31+	2- 3+ 5+ -3 11+ -4  7 -2
Curve Equation t 51150bi1 [1,1,1,-13769063,-26442949219] 1
51150bj (4 curves)	0	2- 3+ 5+ 11+ 31+	2- 3+ 5+  4 11+ -2 -2  4
Curve Equation t 51150bj1 [1,1,1,-37838,2411531] 4 51150bj2 [1,1,1,-165838,-23700469] 4 51150bj3 [1,1,1,206162,-114468469] 2 51150bj4 [1,1,1,-2585838,-1601540469] 2
51150bk (2 curves)	0	2- 3+ 5+ 11+ 31+	2- 3+ 5+  4 11+  6  6 -6
Curve Equation t 51150bk1 [1,1,1,1287,47031] 2 51150bk2 [1,1,1,-14213,574031] 2
51150bl (2 curves)	1	2- 3+ 5+ 11+ 31-	2- 3+ 5+  0 11+ -4 -4  6
Curve Equation t Generators 51150bl1 [1,1,1,-688,3281] 2 [-25:87:1] 51150bl2 [1,1,1,2312,27281] 2 [-5:127:1]
51150bm (2 curves)	1	2- 3+ 5+ 11+ 31-	2- 3+ 5+  2 11+  0 -6 -2
Curve Equation t Generators 51150bm1 [1,1,1,-4288,93281] 2 [25:37:1] 51150bm2 [1,1,1,-66288,6541281] 2 [115:617:1]
51150bn (4 curves)	1	2- 3+ 5+ 11+ 31-	2- 3+ 5+ -2 11+  4 -6  2
Curve Equation t Generators 51150bn1 [1,1,1,-3812213,-2331348469] 2 [-578360:-11555401:512] 51150bn2 [1,1,1,-18707713,29038574531] 2 [13070:419711:8] 51150bn3 [1,1,1,-292472588,-1925321899219] 2 [-1038275852200:533178012901:105154048] 51150bn4 [1,1,1,-292720588,-1921893547219] 2 [-615820:-3714447:64]
51150bo (1 curve)	1	2- 3+ 5+ 11+ 31-	2- 3+ 5+  3 11+  5 -7  0
Curve Equation t Generators 51150bo1 [1,1,1,-4312188,-3470814219] 1 [1509510625:33328749369:571787]
51150bp (2 curves)	0	2- 3+ 5+ 11- 31-	2- 3+ 5+  1 11-  1  3  8
Curve Equation t 51150bp1 [1,1,1,-75713,7987781] 1 51150bp2 [1,1,1,2662,23572031] 1
51150bq (1 curve)	0	2- 3+ 5+ 11- 31-	2- 3+ 5+  2 11-  6  1 -2
Curve Equation t 51150bq1 [1,1,1,112,101] 1
51150br (2 curves)	0	2- 3+ 5+ 11- 31-	2- 3+ 5+ -2 11-  6  4  4
Curve Equation t 51150br1 [1,1,1,-1813,23531] 2 51150br2 [1,1,1,3687,144531] 2
51150bs (2 curves)	0	2- 3+ 5+ 11- 31-	2- 3+ 5+ -4 11-  6 -2 -2
Curve Equation t 51150bs1 [1,1,1,-4230213,-3356780469] 2 51150bs2 [1,1,1,-67718213,-214517868469] 2
51150bt (2 curves)	1	2- 3+ 5- 11+ 31+	2- 3+ 5-  2 11+  2  0  4
Curve Equation t Generators 51150bt1 [1,1,1,-163513,24241031] 2 [19:4588:1] 51150bt2 [1,1,1,-2583513,1597241031] 2 [85:37082:1]
51150bu (1 curve)	1	2- 3+ 5- 11+ 31+	2- 3+ 5- -2 11+  6  3 -6
Curve Equation t Generators 51150bu1 [1,1,1,-2068075638,-36320434211469] 1 [32470630720989:8531874708399655:341532099]
51150bv (1 curve)	1	2- 3+ 5- 11+ 31+	2- 3+ 5-  5 11+ -7 -3  4
Curve Equation t Generators 51150bv1 [1,1,1,-218,-2419] 1 [34140:48631:1728]
51150bw (2 curves)	0	2- 3+ 5- 11- 31+	2- 3+ 5-  2 11-  2  0  4
Curve Equation t 51150bw1 [1,1,1,-779898,-264472569] 2 51150bw2 [1,1,1,-1167098,25153031] 2
51150bx (1 curve)	0	2- 3+ 5- 11- 31+	2- 3+ 5- -2 11- -2  3 -6
Curve Equation t 51150bx1 [1,1,1,-6513013,-8162473969] 1
51150by (1 curve)	0	2- 3+ 5- 11- 31+	2- 3+ 5-  3 11-  3 -7  4
Curve Equation t 51150by1 [1,1,1,-79888,-9032719] 1
51150bz (2 curves)	0	2- 3+ 5- 11- 31+	2- 3+ 5- -4 11- -4  0  4
Curve Equation t 51150bz1 [1,1,1,-12494455513,537551292211031] 2 51150bz2 [1,1,1,-12494478013,537549259336031] 2
51150ca (2 curves)	1	2- 3+ 5- 11- 31-	2- 3+ 5-  0 11- -6 -2 -4
Curve Equation t Generators 51150ca1 [1,1,1,-748,-8119] 2 [145:1647:1] 51150ca2 [1,1,1,-198,-19119] 2 [9236:105903:64]
51150cb (2 curves)	1	2- 3- 5+ 11+ 31+	2- 3- 5+  0 11+  2 -2  2
Curve Equation t Generators 51150cb1 [1,0,0,-258088,-54774208] 2 [992:25304:1] 51150cb2 [1,0,0,-4226088,-3344246208] 2 [-1188:744:1]
51150cc (4 curves)	1	2- 3- 5+ 11+ 31+	2- 3- 5+  0 11+  2 -2 -4
Curve Equation t Generators 51150cc1 [1,0,0,-494088,128127792] 2 [7014:108868:27] 51150cc2 [1,0,0,-7814588,8407613292] 4 [1371273344:-126121421047:2097152] 51150cc3 [1,0,0,-7723838,8612436042] 2 [37600741971846:-1285919445359235:13447314152] 51150cc4 [1,0,0,-125033338,538119144542] 2 [20926:3817537:8]
51150cd (4 curves)	1	2- 3- 5+ 11+ 31+	2- 3- 5+  0 11+  2 -2 -4
Curve Equation t Generators 51150cd1 [1,0,0,-1723151188,27471834990992] 4 [3272:4674764:1] 51150cd2 [1,0,0,-2386703188,4366290798992] 4 [-2872:3347660:1] 51150cd3 [1,0,0,9496464812,34846616718992] 2 [172311104:-124509400084:343] 51150cd4 [1,0,0,-24886703188,-1504866209201008] 2 [-1113068624:30882089404:12167]
51150ce (1 curve)	1	2- 3- 5+ 11+ 31+	2- 3- 5+  3 11+ -4  1 -1
Curve Equation t Generators 51150ce1 [1,0,0,-21923,1855377] 1 [208:2407:1]
51150cf (1 curve)	1	2- 3- 5+ 11+ 31+	2- 3- 5+ -3 11+  2  7  8
Curve Equation t Generators 51150cf1 [1,0,0,-3829938,-2942436258] 1 [1601748:251797551:64]
51150cg (1 curve)	1	2- 3- 5+ 11+ 31+	2- 3- 5+ -3 11+ -4  7 -2
Curve Equation t Generators 51150cg1 [1,0,0,87,2817] 1 [12:69:1]
51150ch (2 curves)	0	2- 3- 5+ 11+ 31-	2- 3- 5+ -2 11+  4 -2 -4
Curve Equation t 51150ch1 [1,0,0,-3188,-145008] 2 51150ch2 [1,0,0,-65188,-6407008] 2
51150ci (4 curves)	0	2- 3- 5+ 11- 31+	2- 3- 5+  0 11-  2 -2  8
Curve Equation t 51150ci1 [1,0,0,-967188,-366193008] 2 51150ci2 [1,0,0,-969188,-364603008] 4 51150ci3 [1,0,0,-303688,-856407508] 2 51150ci4 [1,0,0,-1666688,228969492] 2
51150cj (2 curves)	1	2- 3- 5+ 11- 31-	2- 3- 5+  0 11-  2 -2 -6
Curve Equation t Generators 51150cj1 [1,0,0,14662,2840292] 2 [388:7990:1] 51150cj2 [1,0,0,-233338,40288292] 2 [-238:9194:1]
51150ck (1 curve)	1	2- 3- 5+ 11- 31-	2- 3- 5+  1 11-  0  5 -2
Curve Equation t Generators 51150ck1 [1,0,0,-1475238,689605092] 1 [972:-13686:1]
51150cl (1 curve)	1	2- 3- 5+ 11- 31-	2- 3- 5+ -1 11- -7  5  0
Curve Equation t Generators 51150cl1 [1,0,0,-1565938,-20363664508] 1 [28292:-4766146:1]
51150cm (2 curves)	1	2- 3- 5+ 11- 31-	2- 3- 5+  2 11-  2 -4  0
Curve Equation t Generators 51150cm1 [1,0,0,-4588,-36208] 2 [82:334:1] 51150cm2 [1,0,0,17412,-278208] 2 [1062:34344:1]
51150cn (1 curve)	1	2- 3- 5+ 11- 31-	2- 3- 5+ -3 11-  2  1  0
Curve Equation t Generators 51150cn1 [1,0,0,237626537,1729141358417] 1 [89192:27019529:1]
51150co (1 curve)	1	2- 3- 5+ 11- 31-	2- 3- 5+ -3 11- -2 -7 -4
Curve Equation t Generators 51150co1 [1,0,0,-14588,-4724208] 1 [712:18244:1]
51150cp (2 curves)	1	2- 3- 5+ 11- 31-	2- 3- 5+  4 11- -6  2 -2
Curve Equation t Generators 51150cp1 [1,0,0,-1563,3117] 2 [574:3805:8] 51150cp2 [1,0,0,6187,26367] 2 [10698:140335:216]
51150cq (2 curves)	1	2- 3- 5+ 11- 31-	2- 3- 5+ -4 11-  2  2 -6
Curve Equation t Generators 51150cq1 [1,0,0,-1006638,388565892] 2 [696:-5370:1] 51150cq2 [1,0,0,-882638,487889892] 2 [496:-13370:1]
51150cr (1 curve)	0	2- 3- 5- 11+ 31+	2- 3- 5- -1 11+  1  3 -4
Curve Equation t 51150cr1 [1,0,0,-33,-543] 1
51150cs (2 curves)	0	2- 3- 5- 11+ 31+	2- 3- 5- -2 11+  6 -4  4
Curve Equation t 51150cs1 [1,0,0,-413023,-102193063] 2 51150cs2 [1,0,0,-6608223,-6539005863] 2
51150ct (2 curves)	0	2- 3- 5- 11+ 31+	2- 3- 5-  4 11+  0 -4 -8
Curve Equation t 51150ct1 [1,0,0,-2388,-4608] 2 51150ct2 [1,0,0,-24888,1502892] 2
51150cu (2 curves)	1	2- 3- 5- 11- 31+	2- 3- 5- -4 11-  4  0 -4
Curve Equation t Generators 51150cu1 [1,0,0,-5258,132132] 2 [22:154:1] 51150cu2 [1,0,0,-19658,-919068] 2 [-74:-326:1]
51150cv (1 curve)	0	2- 3- 5- 11- 31-	2- 3- 5-  1 11-  0  5  3
Curve Equation t 51150cv1 [1,0,0,137,-583] 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