Cremona's table of elliptic curves

72912 = 2⁴ · 3 · 7² · 31

Class	r	Atkin-Lehner	Eigenvalues
72912a (1 curve)	1	2+ 3+ 7+ 31+	2+ 3+  0 7+  1  4  3 -5
Curve Equation t Generators 72912a1 [0,-1,0,-1379513,229780629] 1 [-351468:46416027:2197]
72912b (1 curve)	0	2+ 3+ 7+ 31-	2+ 3+ -2 7+  5  4 -1 -1
Curve Equation t 72912b1 [0,-1,0,-8689,-308867] 1
72912c (2 curves)	0	2+ 3+ 7- 31+	2+ 3+  0 7-  2  2  2  4
Curve Equation t 72912c1 [0,-1,0,-171908,27481728] 2 72912c2 [0,-1,0,-145448,36202944] 2
72912d (1 curve)	0	2+ 3+ 7- 31+	2+ 3+  1 7-  0  6  0 -3
Curve Equation t 72912d1 [0,-1,0,180,-657] 1
72912e (1 curve)	0	2+ 3+ 7- 31+	2+ 3+  1 7- -3  3 -1 -5
Curve Equation t 72912e1 [0,-1,0,52120,986448] 1
72912f (1 curve)	0	2+ 3+ 7- 31+	2+ 3+ -1 7-  0  7 -8 -6
Curve Equation t 72912f1 [0,-1,0,-11041,-442931] 1
72912g (1 curve)	0	2+ 3+ 7- 31+	2+ 3+  3 7-  5 -1 -1  7
Curve Equation t 72912g1 [0,-1,0,-1584,-31968] 1
72912h (1 curve)	0	2+ 3+ 7- 31+	2+ 3+ -3 7- -4  2  8  1
Curve Equation t 72912h1 [0,-1,0,45848,-8771069] 1
72912i (2 curves)	0	2+ 3+ 7- 31+	2+ 3+  4 7- -2  6 -6  0
Curve Equation t 72912i1 [0,-1,0,-156,288] 2 72912i2 [0,-1,0,-1416,-19872] 2
72912j (2 curves)	0	2+ 3+ 7- 31+	2+ 3+  4 7- -6  6  6  6
Curve Equation t 72912j1 [0,-1,0,-184256,-30059952] 2 72912j2 [0,-1,0,-343016,29633808] 2
72912k (2 curves)	0	2+ 3+ 7- 31+	2+ 3+ -4 7- -6 -2 -2  0
Curve Equation t 72912k1 [0,-1,0,425,223126] 2 72912k2 [0,-1,0,-52740,4582656] 2
72912l (2 curves)	1	2+ 3+ 7- 31-	2+ 3+  0 7- -2  2  2  2
Curve Equation t Generators 72912l1 [0,-1,0,-14128,-139376] 2 [286:4374:1] 72912l2 [0,-1,0,-172888,-27573104] 2 [-240:196:1]
72912m (2 curves)	1	2+ 3+ 7- 31-	2+ 3+  0 7- -2  6 -6  0
Curve Equation t Generators 72912m1 [0,-1,0,-5868,-171072] 2 [404:7952:1] 72912m2 [0,-1,0,-6008,-162336] 2 [-35:62:1]
72912n (1 curve)	1	2+ 3+ 7- 31-	2+ 3+ -1 7-  2 -4  4 -7
Curve Equation t Generators 72912n1 [0,-1,0,-6876,244539] 1 [27:279:1]
72912o (1 curve)	1	2+ 3+ 7- 31-	2+ 3+ -1 7- -3  1 -1  3
Curve Equation t Generators 72912o1 [0,-1,0,-24464736,-99771505056] 1 [70978402612:7960645474068:4826809]
72912p (4 curves)	1	2+ 3+ 7- 31-	2+ 3+  2 7-  0 -2  2  0
Curve Equation t Generators 72912p1 [0,-1,0,-4132,-94688] 2 [-1916:2295:64] 72912p2 [0,-1,0,-12952,455680] 4 [-35:930:1] 72912p3 [0,-1,0,28208,2727712] 4 [1818:36505:8] 72912p4 [0,-1,0,-195232,33266080] 2 [357:2990:1]
72912q (1 curve)	1	2+ 3+ 7- 31-	2+ 3+ -3 7-  4 -3  0  0
Curve Equation t Generators 72912q1 [0,-1,0,-457,47461] 1 [180:2401:1]
72912r (2 curves)	1	2+ 3- 7- 31+	2+ 3-  0 7- -2 -6  6  0
Curve Equation t Generators 72912r1 [0,1,0,-287548,59252780] 2 [311:48:1] 72912r2 [0,1,0,-294408,56270052] 2 [216:1674:1]
72912s (1 curve)	1	2+ 3- 7- 31+	2+ 3-  1 7-  4  2  0  1
Curve Equation t Generators 72912s1 [0,1,0,-4720,123647] 1 [41:27:1]
72912t (2 curves)	1	2+ 3- 7- 31+	2+ 3-  2 7-  0  2  6  6
Curve Equation t Generators 72912t1 [0,1,0,-3152,-65052] 2 [-38:36:1] 72912t2 [0,1,0,2728,-274380] 2 [60:330:1]
72912u (4 curves)	1	2+ 3- 7- 31+	2+ 3-  2 7- -4  2 -2 -8
Curve Equation t Generators 72912u1 [0,1,0,-51172,-3453892] 2 [-178:216:1] 72912u2 [0,1,0,-765592,-258073180] 4 [1066:11760:1] 72912u3 [0,1,0,-712672,-295223020] 2 [8474:94485:8] 72912u4 [0,1,0,-12249232,-16505127052] 2 [-54566970:-5851:27000]
72912v (4 curves)	1	2+ 3- 7- 31+	2+ 3-  2 7- -4  2 -6  4
Curve Equation t Generators 72912v1 [0,1,0,-13687,-620908] 2 [54220:1084272:125] 72912v2 [0,1,0,-13932,-597780] 4 [-57:120:1] 72912v3 [0,1,0,12528,-2576988] 2 [114:588:1] 72912v4 [0,1,0,-44312,2865540] 2 [-80:2430:1]
72912w (1 curve)	1	2+ 3- 7- 31+	2+ 3-  2 7-  5 -4  1  1
Curve Equation t Generators 72912w1 [0,1,0,-425777,106792923] 1 [10074:2897:27]
72912x (4 curves)	1	2+ 3- 7- 31+	2+ 3- -2 7- -4 -2  2  4
Curve Equation t Generators 72912x1 [0,1,0,-2319,-30360] 2 [-8312:29289:512] 72912x2 [0,1,0,-14324,632316] 4 [31:468:1] 72912x3 [0,1,0,6256,2319876] 2 [4953:83980:27] 72912x4 [0,1,0,-226984,41548100] 4 [128:3822:1]
72912y (1 curve)	1	2+ 3- 7- 31+	2+ 3-  3 7-  4  3  0  0
Curve Equation t Generators 72912y1 [0,1,0,-9,-141] 1 [590:14343:1]
72912z (1 curve)	0	2+ 3- 7- 31-	2+ 3-  0 7-  1 -4 -3  5
Curve Equation t 72912z1 [0,1,0,-67596153,-78679563453] 1
72912ba (2 curves)	0	2+ 3- 7- 31-	2+ 3-  0 7-  2  6 -2  4
Curve Equation t 72912ba1 [0,1,0,-3348,72540] 2 72912ba2 [0,1,0,-408,198372] 2
72912bb (2 curves)	0	2+ 3- 7- 31-	2+ 3-  0 7- -2  2  6  8
Curve Equation t 72912bb1 [0,1,0,-3103,98804] 2 72912bb2 [0,1,0,-56268,5117580] 2
72912bc (1 curve)	0	2+ 3- 7- 31-	2+ 3-  3 7-  0 -3  4  6
Curve Equation t 72912bc1 [0,1,0,453871,-1217799381] 1
72912bd (1 curve)	0	2+ 3- 7- 31-	2+ 3-  3 7-  6  0  4 -3
Curve Equation t 72912bd1 [0,1,0,376,29763] 1
72912be (2 curves)	0	2+ 3- 7- 31-	2+ 3- -4 7- -2 -6  6  0
Curve Equation t 72912be1 [0,1,0,-7660,-83476] 2 72912be2 [0,1,0,-69400,6954884] 2
72912bf (2 curves)	0	2- 3+ 7+ 31+	2- 3+  0 7+ -3 -4  3  7
Curve Equation t 72912bf1 [0,-1,0,-4573,-104831] 1 72912bf2 [0,-1,0,-86893,9872353] 1
72912bg (1 curve)	1	2- 3+ 7+ 31-	2- 3+  4 7+ -3  0 -3  1
Curve Equation t Generators 72912bg1 [0,-1,0,-261,813] 1 [84:125:27]
72912bh (1 curve)	1	2- 3+ 7- 31+	2- 3+  1 7-  0 -1  4  2
Curve Equation t Generators 72912bh1 [0,-1,0,-1045,-23687] 1 [593:14406:1]
72912bi (2 curves)	1	2- 3+ 7- 31+	2- 3+  2 7-  0  6  6 -2
Curve Equation t Generators 72912bi1 [0,-1,0,-36472,1841008] 2 [13:1170:1] 72912bi2 [0,-1,0,-530392,148831600] 2 [82:10290:1]
72912bj (2 curves)	1	2- 3+ 7- 31+	2- 3+  2 7- -2 -4 -8 -4
Curve Equation t Generators 72912bj1 [0,-1,0,-4387672,-3548465360] 2 [3323236:318702840:343] 72912bj2 [0,-1,0,-70271112,-226708853328] 2 [37059272879538:2247214137039810:3222118333]
72912bk (4 curves)	1	2- 3+ 7- 31+	2- 3+ -2 7-  0  2 -2  8
Curve Equation t Generators 72912bk1 [0,-1,0,-2851424,1803618048] 2 [2162:75762:1] 72912bk2 [0,-1,0,-6865504,-4397332736] 4 [19985520:-17194449664:27] 72912bk3 [0,-1,0,20354976,-30637875456] 2 [16024246513214526:344722601806876350:11346637993111] 72912bk4 [0,-1,0,-98311264,-375081865472] 2 [-156336:36064:27]
72912bl (2 curves)	1	2- 3+ 7- 31+	2- 3+ -4 7- -2  2 -2  8
Curve Equation t Generators 72912bl1 [0,-1,0,-2760,31536] 2 [68:-392:1] 72912bl2 [0,-1,0,9000,219696] 2 [26:-686:1]
72912bm (2 curves)	2	2- 3+ 7- 31-	2- 3+  0 7- -2 -2 -2 -4
Curve Equation t Generators 72912bm1 [0,-1,0,-688,-6656] 2 [-15:8:1]&[-14:6:1] 72912bm2 [0,-1,0,-1248,6336] 2 [-30:126:1]&[5:14:1]
72912bn (1 curve)	0	2- 3+ 7- 31-	2- 3+  1 7-  0  6  8  7
Curve Equation t 72912bn1 [0,-1,0,-310,2479] 1
72912bo (1 curve)	0	2- 3+ 7- 31-	2- 3+  1 7- -3 -3 -1  7
Curve Equation t 72912bo1 [0,-1,0,-65480,-7316112] 1
72912bp (1 curve)	0	2- 3+ 7- 31-	2- 3+ -1 7-  4 -5  0 -4
Curve Equation t 72912bp1 [0,-1,0,-2501,-47571] 1
72912bq (1 curve)	0	2- 3+ 7- 31-	2- 3+ -1 7-  5  5  3 -1
Curve Equation t 72912bq1 [0,-1,0,-16,201664] 1
72912br (1 curve)	0	2- 3+ 7- 31-	2- 3+  2 7- -1 -4 -3 -1
Curve Equation t 72912br1 [0,-1,0,-597,477] 1
72912bs (2 curves)	0	2- 3+ 7- 31-	2- 3+  2 7-  2 -4  0 -4
Curve Equation t 72912bs1 [0,-1,0,22405528,3499083120] 2 72912bs2 [0,-1,0,-89988712,28135900528] 2
72912bt (2 curves)	0	2- 3+ 7- 31-	2- 3+  2 7-  4  2 -6 -2
Curve Equation t 72912bt1 [0,-1,0,-3932952,2841595632] 2 72912bt2 [0,-1,0,-11835672,-12154605840] 2
72912bu (6 curves)	0	2- 3+ 7- 31-	2- 3+  2 7- -4  2  6 -4
Curve Equation t 72912bu1 [0,-1,0,-81552,-1064457792] 2 72912bu2 [0,-1,0,-16137872,-24609445440] 4 72912bu3 [0,-1,0,-31943312,31518833088] 4 72912bu4 [0,-1,0,-257233552,-1587873834560] 4 72912bu5 [0,-1,0,-256261392,-1600472250432] 2 72912bu6 [0,-1,0,-4115736592,-101628053853248] 2
72912bv (2 curves)	0	2- 3+ 7- 31-	2- 3+ -2 7-  0  2  2 -2
Curve Equation t 72912bv1 [0,-1,0,-24264,-1432080] 2 72912bv2 [0,-1,0,-387144,-92587536] 2
72912bw (2 curves)	0	2- 3+ 7- 31-	2- 3+ -2 7-  0  6  2 -2
Curve Equation t 72912bw1 [0,-1,0,-148584,-19358352] 2 72912bw2 [0,-1,0,227736,-101847696] 2
72912bx (1 curve)	0	2- 3+ 7- 31-	2- 3+ -3 7-  4  7  4  8
Curve Equation t 72912bx1 [0,-1,0,316923,-69209811] 1
72912by (2 curves)	0	2- 3+ 7- 31-	2- 3+  4 7-  6  2  2 -8
Curve Equation t 72912by1 [0,-1,0,-148976,7301568] 2 72912by2 [0,-1,0,-1905136,1011825088] 2
72912bz (2 curves)	0	2- 3+ 7- 31-	2- 3+ -4 7-  2  2 -6  2
Curve Equation t 72912bz1 [0,-1,0,-8528760,9589558896] 2 72912bz2 [0,-1,0,-8811000,8921214576] 2
72912ca (1 curve)	1	2- 3- 7+ 31+	2- 3- -2 7+ -1  4  3  1
Curve Equation t Generators 72912ca1 [0,1,0,-29269,-105085] 1 [-82:1323:1]
72912cb (2 curves)	0	2- 3- 7- 31+	2- 3-  0 7-  0  0  2 -4
Curve Equation t 72912cb1 [0,1,0,-1633,-25558] 2 72912cb2 [0,1,0,-3348,35496] 2
72912cc (2 curves)	0	2- 3- 7- 31+	2- 3-  0 7- -2  2  2  4
Curve Equation t 72912cc1 [0,1,0,-33728,2350452] 2 72912cc2 [0,1,0,-61168,-2050924] 2
72912cd (2 curves)	0	2- 3- 7- 31+	2- 3-  0 7- -2 -2 -2 -2
Curve Equation t 72912cd1 [0,1,0,-4990568,3790999092] 2 72912cd2 [0,1,0,-77244008,261273357876] 2
72912ce (2 curves)	0	2- 3- 7- 31+	2- 3-  0 7-  4  4 -2  4
Curve Equation t 72912ce1 [0,1,0,-1112953,-452254594] 2 72912ce2 [0,1,0,-1196988,-380085336] 2
72912cf (1 curve)	0	2- 3- 7- 31+	2- 3-  1 7-  4  5  0  4
Curve Equation t 72912cf1 [0,1,0,-122565,16561971] 1
72912cg (1 curve)	0	2- 3- 7- 31+	2- 3- -1 7- -1 -5  5 -5
Curve Equation t 72912cg1 [0,1,0,-180336,-29537964] 1
72912ch (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  0  2  6  2
Curve Equation t 72912ch1 [0,1,0,-7366872,-6938688492] 2 72912ch2 [0,1,0,9779208,-34434142380] 2
72912ci (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  0 -2 -2  2
Curve Equation t 72912ci1 [0,1,0,-1188952,493581332] 2 72912ci2 [0,1,0,-18970072,31795464980] 2
72912cj (4 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  0  6 -6 -4
Curve Equation t 72912cj1 [0,1,0,28208,-1834540] 2 72912cj2 [0,1,0,-163872,-17585100] 4 72912cj3 [0,1,0,-1014512,379493652] 4 72912cj4 [0,1,0,-2386512,-1419626412] 2
72912ck (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  6 -4  0 -4
Curve Equation t 72912ck1 [0,1,0,-24712,2469620] 2 72912ck2 [0,1,0,-463752,121361652] 2
72912cl (2 curves)	0	2- 3- 7- 31+	2- 3- -2 7-  4 -2  6  2
Curve Equation t 72912cl1 [0,1,0,-80264,-8307468] 2 72912cl2 [0,1,0,-241544,35367156] 2
72912cm (1 curve)	0	2- 3- 7- 31+	2- 3-  3 7- -2  4  4 -5
Curve Equation t 72912cm1 [0,1,0,-114,3303] 1
72912cn (1 curve)	0	2- 3- 7- 31+	2- 3-  3 7-  3  3  5 -1
Curve Equation t 72912cn1 [0,1,0,-981584,412553364] 1
72912co (1 curve)	0	2- 3- 7- 31+	2- 3-  3 7-  4 -7 -4 -8
Curve Equation t 72912co1 [0,1,0,15529211,23707906739] 1
72912cp (1 curve)	0	2- 3- 7- 31+	2- 3- -3 7- -5  7  1  7
Curve Equation t 72912cp1 [0,1,0,-12952,-583276] 1
72912cq (2 curves)	0	2- 3- 7- 31+	2- 3- -4 7-  2 -2  8  4
Curve Equation t 72912cq1 [0,1,0,211615,-49701366] 2 72912cq2 [0,1,0,-1436500,-507877336] 2
72912cr (1 curve)	0	2- 3- 7- 31+	2- 3- -4 7- -3  0  3 -1
Curve Equation t 72912cr1 [0,1,0,-12805,-253261] 1
72912cs (2 curves)	0	2- 3- 7- 31+	2- 3- -4 7-  6 -2 -2  8
Curve Equation t 72912cs1 [0,1,0,-3040,-22156] 2 72912cs2 [0,1,0,-38880,-2961036] 2
72912ct (4 curves)	1	2- 3- 7- 31-	2- 3-  0 7-  0  4  6 -4
Curve Equation t Generators 72912ct1 [0,1,0,-19273,-801130] 2 [-7036:2073:64] 72912ct2 [0,1,0,-103308,12073032] 2 [-369:294:1] 72912ct3 [0,1,0,-1459873,-679410166] 2 [-273322711912972:-257716348821:391580530496] 72912ct4 [0,1,0,-1461588,-677735640] 2 [-21893223:-4527306:29791]
72912cu (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7- -3  4 -3 -7
Curve Equation t Generators 72912cu1 [0,1,0,-93,279] 1 [3:6:1] 72912cu2 [0,1,0,-1773,-29289] 1 [-25:6:1]
72912cv (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7-  6  2 -6  6
Curve Equation t Generators 72912cv1 [0,1,0,-8248,65876] 2 [-61:588:1] 72912cv2 [0,1,0,-78808,-8485996] 2 [-157:204:1]
72912cw (4 curves)	1	2- 3- 7- 31-	2- 3-  0 7- -6 -2 -6 -4
Curve Equation t Generators 72912cw1 [0,1,0,-145448,17770164] 2 [100:2058:1] 72912cw2 [0,1,0,277912,102272820] 2 [-68:9114:1] 72912cw3 [0,1,0,-3355928,-2365591404] 2 [-1076:882:1] 72912cw4 [0,1,0,-2603288,-3454510956] 2 [2508:76146:1]
72912cx (2 curves)	1	2- 3- 7- 31-	2- 3- -1 7-  3  1 -3 -5
Curve Equation t Generators 72912cx1 [0,1,0,11744,174068] 1 [44:-882:1] 72912cx2 [0,1,0,-1093696,-440825932] 1 [1276:15582:1]
72912cy (2 curves)	1	2- 3- 7- 31-	2- 3-  2 7-  0 -2  0  4
Curve Equation t Generators 72912cy1 [0,1,0,-457,5018] 2 [-366:2548:27] 72912cy2 [0,1,0,-8052,275400] 2 [187500:1436435:1728]
72912cz (4 curves)	1	2- 3- 7- 31-	2- 3-  2 7-  0 -2 -6  4
Curve Equation t Generators 72912cz1 [0,1,0,-1567232,-755680332] 2 [138291098682:-119502980495360:185193] 72912cz2 [0,1,0,-1629952,-691981900] 4 [9963182:18627840:6859] 72912cz3 [0,1,0,2744768,-3763035340] 2 [3530:223440:1] 72912cz4 [0,1,0,-7008192,6456774708] 4 [1124:930:1]
72912da (2 curves)	1	2- 3- 7- 31-	2- 3-  2 7-  2  4  0 -4
Curve Equation t Generators 72912da1 [0,1,0,2728,-109740] 2 [471:10290:1] 72912da2 [0,1,0,-24712,-1284172] 2 [-68:294:1]
72912db (2 curves)	1	2- 3- 7- 31-	2- 3- -2 7-  0 -6 -6  2
Curve Equation t Generators 72912db1 [0,1,0,-744,-5580] 2 [-18:48:1] 72912db2 [0,1,0,-10824,-437004] 2 [-60:6:1]
72912dc (4 curves)	1	2- 3- 7- 31-	2- 3- -2 7- -4 -2  2  0
Curve Equation t Generators 72912dc1 [0,1,0,-32944,-2304940] 2 [-101:48:1] 72912dc2 [0,1,0,-48624,97236] 4 [-124:2058:1] 72912dc3 [0,1,0,194416,972180] 2 [58:3528:1] 72912dc4 [0,1,0,-542544,153212436] 4 [884:19110:1]
72912dd (3 curves)	1	2- 3- 7- 31-	2- 3-  3 7-  0 -5  0  2
Curve Equation t Generators 72912dd1 [0,1,0,17771,-1977277] 1 [86:441:1] 72912dd2 [0,1,0,-828949,-291301501] 1 [1430:38073:1] 72912dd3 [0,1,0,-67178869,-211954691677] 1 [341686:199671129:1]
72912de (2 curves)	1	2- 3- 7- 31-	2- 3- -3 7-  0 -2  0 -1
Curve Equation t Generators 72912de1 [0,1,0,-149662,-23479849] 1 [1403:50301:1] 72912de2 [0,1,0,-12294802,-16597309429] 1 [6107:368943:1]
72912df (1 curve)	1	2- 3- 7- 31-	2- 3- -3 7-  0  5  0  6
Curve Equation t Generators 72912df1 [0,1,0,4443,2309439] 1 [-1059:38906:27]
72912dg (2 curves)	1	2- 3- 7- 31-	2- 3- -3 7-  3  1 -3 -1
Curve Equation t Generators 72912dg1 [0,1,0,57608,118474964] 1 [-250:9408:1] 72912dg2 [0,1,0,-518632,-3204124876] 1 [182586:14852096:27]

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