Cremona's table of elliptic curves

64320 = 2⁶ · 3 · 5 · 67

Class	r	Atkin-Lehner	Eigenvalues
64320a (2 curves)	1	2+ 3+ 5+ 67+	2+ 3+ 5+  2 -4  4  2  4
Curve Equation t Generators 64320a1 [0,-1,0,-201,201] 2 [-1:20:1] 64320a2 [0,-1,0,799,801] 2 [1:40:1]
64320b (2 curves)	1	2+ 3+ 5+ 67+	2+ 3+ 5+ -4  0  4  0  4
Curve Equation t Generators 64320b1 [0,-1,0,-241,-1295] 2 [-9:8:1] 64320b2 [0,-1,0,159,-5535] 2 [31:168:1]
64320c (4 curves)	0	2+ 3+ 5+ 67-	2+ 3+ 5+  0  0 -6  2  4
Curve Equation t 64320c1 [0,-1,0,4,-57954] 2 64320c2 [0,-1,0,-22441,-1265495] 4 64320c3 [0,-1,0,-46561,1961761] 2 64320c4 [0,-1,0,-357441,-82134495] 2
64320d (1 curve)	2	2+ 3+ 5+ 67-	2+ 3+ 5+ -1 -3 -2 -2 -6
Curve Equation t Generators 64320d1 [0,-1,0,-321,-3519] 1 [24:45:1]&[33:144:1]
64320e (2 curves)	0	2+ 3+ 5+ 67-	2+ 3+ 5+ -2  4  0  2  4
Curve Equation t 64320e1 [0,-1,0,-17441,-619359] 2 64320e2 [0,-1,0,46559,-4164959] 2
64320f (2 curves)	0	2+ 3+ 5+ 67-	2+ 3+ 5+  4 -2 -6 -4  4
Curve Equation t 64320f1 [0,-1,0,-32321,-2330559] 2 64320f2 [0,-1,0,-523841,-145756095] 2
64320g (2 curves)	0	2+ 3+ 5+ 67-	2+ 3+ 5+  4 -6  2  0  4
Curve Equation t 64320g1 [0,-1,0,159,5985] 2 64320g2 [0,-1,0,-4161,100161] 2
64320h (4 curves)	0	2+ 3+ 5- 67+	2+ 3+ 5-  2  0 -2  0 -8
Curve Equation t 64320h1 [0,-1,0,-57025,4522177] 2 64320h2 [0,-1,0,-876225,315982017] 2 64320h3 [0,-1,0,-1224385,-520531775] 2 64320h4 [0,-1,0,-1544385,-226835775] 2
64320i (2 curves)	0	2+ 3+ 5- 67+	2+ 3+ 5-  2  6 -2 -3  1
Curve Equation t 64320i1 [0,-1,0,955,1407] 1 64320i2 [0,-1,0,-12005,-555225] 1
64320j (2 curves)	0	2+ 3+ 5- 67+	2+ 3+ 5- -2  0 -6  0  0
Curve Equation t 64320j1 [0,-1,0,-195425,-33186975] 2 64320j2 [0,-1,0,-196225,-32900735] 2
64320k (2 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5-  0  2  2  0  4
Curve Equation t Generators 64320k1 [0,-1,0,-193225,-251661623] 2 [29883:805040:27] 64320k2 [0,-1,0,-7279105,-7517522975] 2 [4565:233160:1]
64320l (2 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5-  0 -4 -4  0  4
Curve Equation t Generators 64320l1 [0,-1,0,-60,270] 2 [7:12:1] 64320l2 [0,-1,0,-1065,13737] 2 [17:16:1]
64320m (1 curve)	1	2+ 3+ 5- 67-	2+ 3+ 5-  2  0  0 -3 -5
Curve Equation t Generators 64320m1 [0,-1,0,-255,-1503] 1 [24:75:1]
64320n (1 curve)	1	2+ 3+ 5- 67-	2+ 3+ 5- -2  2 -2  5 -1
Curve Equation t Generators 64320n1 [0,-1,0,-85,2317] 1 [4:45:1]
64320o (2 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5- -2  4  0 -2 -4
Curve Equation t Generators 64320o1 [0,-1,0,-14783465,-21477303063] 2 [7029:471000:1] 64320o2 [0,-1,0,841535,-64605428063] 2 [180408:-13207625:27]
64320p (2 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5- -2  4  2  0  8
Curve Equation t Generators 64320p1 [0,-1,0,-209025,36354177] 2 [-3291:209152:27] 64320p2 [0,-1,0,-413825,-46344063] 2 [-475653057:-12594651904:2146689]
64320q (4 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5-  4  4 -6 -2  4
Curve Equation t Generators 64320q1 [0,-1,0,-2545,-48143] 2 [59:60:1] 64320q2 [0,-1,0,-4545,40257] 4 [16344:2089395:1] 64320q3 [0,-1,0,17055,295137] 2 [-147273:1298044:9261] 64320q4 [0,-1,0,-58145,5410977] 2 [5606216:-716633973:343]
64320r (4 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5-  4 -4 -2  2 -4
Curve Equation t Generators 64320r1 [0,-1,0,-4906145,-4180805343] 2 [-116557821575504742888:-48124771101164723615:91168746998773248] 64320r2 [0,-1,0,-5233825,-3590129375] 4 [-26112898980:-392903296435:16003008] 64320r3 [0,-1,0,11918175,-22213770975] 2 [2484689082657998580:-145897433938549363825:1047410108087616] 64320r4 [0,-1,0,-27628705,52831531297] 4 [11030253:442928000:2197]
64320s (2 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5- -4  0  4 -4 -4
Curve Equation t Generators 64320s1 [0,-1,0,-1985,-26175] 2 [-33:48:1] 64320s2 [0,-1,0,4415,-165695] 2 [1029:6416:27]
64320t (4 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5- -4  4 -2 -6  4
Curve Equation t Generators 64320t1 [0,-1,0,-6705,-209103] 2 [529:12000:1] 64320t2 [0,-1,0,-6785,-203775] 4 [-40:45:1] 64320t3 [0,-1,0,3935,-797663] 2 [169:2160:1] 64320t4 [0,-1,0,-18785,729825] 4 [120:435:1]
64320u (2 curves)	1	2+ 3+ 5- 67-	2+ 3+ 5- -4  6 -6  0  4
Curve Equation t Generators 64320u1 [0,-1,0,-5385,197577] 2 [13:360:1] 64320u2 [0,-1,0,-92865,10922625] 2 [41:2680:1]
64320v (4 curves)	0	2+ 3- 5+ 67+	2+ 3- 5+  0  0 -6  2 -4
Curve Equation t 64320v1 [0,1,0,4,57954] 2 64320v2 [0,1,0,-22441,1265495] 4 64320v3 [0,1,0,-46561,-1961761] 2 64320v4 [0,1,0,-357441,82134495] 2
64320w (2 curves)	0	2+ 3- 5+ 67+	2+ 3- 5+  0 -2  2 -4 -4
Curve Equation t 64320w1 [0,1,0,319,1695] 2 64320w2 [0,1,0,-1601,13599] 2
64320x (2 curves)	0	2+ 3- 5+ 67+	2+ 3- 5+  2  0 -2 -4  8
Curve Equation t 64320x1 [0,1,0,-481,1919] 2 64320x2 [0,1,0,-3681,-85761] 2
64320y (2 curves)	0	2+ 3- 5+ 67+	2+ 3- 5+ -2  0  2  4  0
Curve Equation t 64320y1 [0,1,0,-55041,745695] 2 64320y2 [0,1,0,-555041,-158554305] 2
64320z (1 curve)	0	2+ 3- 5+ 67+	2+ 3- 5+ -3  5 -2  6 -2
Curve Equation t 64320z1 [0,1,0,-17988321,51931146879] 1
64320ba (2 curves)	1	2+ 3- 5+ 67-	2+ 3- 5+  0  0 -4 -4 -4
Curve Equation t Generators 64320ba1 [0,1,0,-19041,-938241] 2 [-93:192:1] 64320ba2 [0,1,0,20959,-4322241] 2 [157:1692:1]
64320bb (1 curve)	1	2+ 3- 5+ 67-	2+ 3- 5+ -1  1  6 -2  2
Curve Equation t Generators 64320bb1 [0,1,0,-5121,1154655] 1 [171:2304:1]
64320bc (1 curve)	1	2+ 3- 5+ 67-	2+ 3- 5+  2 -2 -2 -7 -1
Curve Equation t Generators 64320bc1 [0,1,0,-31941,2186595] 1 [102:15:1]
64320bd (2 curves)	1	2+ 3- 5+ 67-	2+ 3- 5+ -2  4  4  2 -4
Curve Equation t Generators 64320bd1 [0,1,0,-201,-201] 2 [35:192:1] 64320bd2 [0,1,0,799,-801] 2 [7:72:1]
64320be (2 curves)	1	2+ 3- 5+ 67-	2+ 3- 5+ -2  4 -6  4  0
Curve Equation t Generators 64320be1 [0,1,0,-321,-2145] 2 [77:660:1] 64320be2 [0,1,0,-1121,11775] 2 [-29:144:1]
64320bf (4 curves)	1	2+ 3- 5+ 67-	2+ 3- 5+ -4  4 -2  2 -4
Curve Equation t Generators 64320bf1 [0,1,0,-3601,-63985] 2 [-1095:3520:27] 64320bf2 [0,1,0,-53601,-4793985] 4 [6751771:246576000:4913] 64320bf3 [0,1,0,-49601,-5535585] 4 [5467:403920:1] 64320bf4 [0,1,0,-857601,-305972385] 2 [59721993140:1713892431669:39304000]
64320bg (4 curves)	1	2+ 3- 5- 67+	2+ 3- 5-  0  0 -2  2  4
Curve Equation t Generators 64320bg1 [0,1,0,15,9135] 2 [3:96:1] 64320bg2 [0,1,0,-6465,194463] 4 [57:120:1] 64320bg3 [0,1,0,-13665,-325377] 2 [297:4680:1] 64320bg4 [0,1,0,-102945,12678975] 4 [2730:33375:8]
64320bh (2 curves)	1	2+ 3- 5- 67+	2+ 3- 5-  0 -2  2  0 -4
Curve Equation t Generators 64320bh1 [0,1,0,-193225,251661623] 2 [-409:16200:1] 64320bh2 [0,1,0,-7279105,7517522975] 2 [-1885:120600:1]
64320bi (4 curves)	1	2+ 3- 5- 67+	2+ 3- 5-  0  4  2 -6 -4
Curve Equation t Generators 64320bi1 [0,1,0,2115,538083] 2 [-9:720:1] 64320bi2 [0,1,0,-87665,9641775] 4 [-125:4320:1] 64320bi3 [0,1,0,-221665,-27047425] 2 [905:22680:1] 64320bi4 [0,1,0,-1390145,630403743] 2 [691:480:1]
64320bj (2 curves)	1	2+ 3- 5- 67+	2+ 3- 5-  0  4 -4  0 -4
Curve Equation t Generators 64320bj1 [0,1,0,-60,-270] 2 [1026861:-5349878:35937] 64320bj2 [0,1,0,-1065,-13737] 2 [3117:32120:27]
64320bk (4 curves)	1	2+ 3- 5- 67+	2+ 3- 5-  0 -4 -2  6  4
Curve Equation t Generators 64320bk1 [0,1,0,8095,-161025] 2 [25:240:1] 64320bk2 [0,1,0,-37985,-1423617] 4 [1561:61200:1] 64320bk3 [0,1,0,-295265,60683775] 2 [435:3840:1] 64320bk4 [0,1,0,-517985,-143599617] 2 [44067:1565360:27]
64320bl (2 curves)	1	2+ 3- 5- 67+	2+ 3- 5-  2 -4  0 -2  4
Curve Equation t Generators 64320bl1 [0,1,0,-14783465,21477303063] 2 [1471:54000:1] 64320bl2 [0,1,0,841535,64605428063] 2 [7721:729000:1]
64320bm (1 curve)	1	2+ 3- 5- 67+	2+ 3- 5- -2  0  0 -3  5
Curve Equation t Generators 64320bm1 [0,1,0,-255,1503] 1 [6:15:1]
64320bn (2 curves)	1	2+ 3- 5- 67+	2+ 3- 5-  4 -6 -6  0 -4
Curve Equation t Generators 64320bn1 [0,1,0,-5385,-197577] 2 [123:1008:1] 64320bn2 [0,1,0,-92865,-10922625] 2 [-177:24:1]
64320bo (2 curves)	2	2- 3+ 5+ 67+	2- 3+ 5+  0  0 -4 -4  4
Curve Equation t Generators 64320bo1 [0,-1,0,-19041,938241] 2 [-64:1375:1]&[29:640:1] 64320bo2 [0,-1,0,20959,4322241] 2 [13:-2144:1]&[279:5640:1]
64320bp (1 curve)	0	2- 3+ 5+ 67+	2- 3+ 5+  1 -1  6 -2 -2
Curve Equation t 64320bp1 [0,-1,0,-5121,-1154655] 1
64320bq (2 curves)	2	2- 3+ 5+ 67+	2- 3+ 5+  2 -4 -6  4  0
Curve Equation t Generators 64320bq1 [0,-1,0,-321,2145] 2 [-19:32:1]&[-5:60:1] 64320bq2 [0,-1,0,-1121,-11775] 2 [-24:27:1]&[-19:48:1]
64320br (1 curve)	0	2- 3+ 5+ 67+	2- 3+ 5+ -2  2 -2 -7  1
Curve Equation t 64320br1 [0,-1,0,-31941,-2186595] 1
64320bs (4 curves)	0	2- 3+ 5+ 67+	2- 3+ 5+  4 -4 -2  2  4
Curve Equation t 64320bs1 [0,-1,0,-3601,63985] 2 64320bs2 [0,-1,0,-53601,4793985] 4 64320bs3 [0,-1,0,-49601,5535585] 2 64320bs4 [0,-1,0,-857601,305972385] 4
64320bt (2 curves)	1	2- 3+ 5+ 67-	2- 3+ 5+  0  2  2 -4  4
Curve Equation t Generators 64320bt1 [0,-1,0,319,-1695] 2 [59:468:1] 64320bt2 [0,-1,0,-1601,-13599] 2 [-27:96:1]
64320bu (4 curves)	1	2- 3+ 5+ 67-	2- 3+ 5+  0 -4  2  2  0
Curve Equation t Generators 64320bu1 [0,-1,0,-1676,17730] 2 [90:105:8] 64320bu2 [0,-1,0,-24121,1449721] 4 [64:405:1] 64320bu3 [0,-1,0,-21441,1781505] 2 [2721:21500:27] 64320bu4 [0,-1,0,-385921,92406241] 2 [9768:2465:27]
64320bv (2 curves)	1	2- 3+ 5+ 67-	2- 3+ 5+  2  0  2  4  0
Curve Equation t Generators 64320bv1 [0,-1,0,-55041,-745695] 2 [119545:-3580352:125] 64320bv2 [0,-1,0,-555041,158554305] 2 [3805:230480:1]
64320bw (2 curves)	1	2- 3+ 5+ 67-	2- 3+ 5+ -2  0 -2 -4 -8
Curve Equation t Generators 64320bw1 [0,-1,0,-481,-1919] 2 [-9:40:1] 64320bw2 [0,-1,0,-3681,85761] 2 [45:96:1]
64320bx (1 curve)	1	2- 3+ 5+ 67-	2- 3+ 5+ -2  0  4 -3 -1
Curve Equation t Generators 64320bx1 [0,-1,0,1709,-46259] 1 [2404:16875:64]
64320by (1 curve)	1	2- 3+ 5+ 67-	2- 3+ 5+  3 -5 -2  6  2
Curve Equation t Generators 64320by1 [0,-1,0,-17988321,-51931146879] 1 [3085051649971356646059813:193690068376303482406059204:419683536815256340271]
64320bz (2 curves)	1	2- 3+ 5- 67+	2- 3+ 5- -2 -4  2  4  4
Curve Equation t Generators 64320bz1 [0,-1,0,-2745,-51975] 2 [-25:20:1] 64320bz2 [0,-1,0,-7745,197025] 2 [125:-1080:1]
64320ca (1 curve)	1	2- 3+ 5- 67+	2- 3+ 5-  3 -3  6 -6 -2
Curve Equation t Generators 64320ca1 [0,-1,0,2975,-17375] 1 [40:405:1]
64320cb (4 curves)	0	2- 3+ 5- 67-	2- 3+ 5-  0  0 -2  2 -4
Curve Equation t 64320cb1 [0,-1,0,15,-9135] 2 64320cb2 [0,-1,0,-6465,-194463] 4 64320cb3 [0,-1,0,-13665,325377] 4 64320cb4 [0,-1,0,-102945,-12678975] 2
64320cc (4 curves)	0	2- 3+ 5- 67-	2- 3+ 5-  0  4 -2  6 -4
Curve Equation t 64320cc1 [0,-1,0,8095,161025] 2 64320cc2 [0,-1,0,-37985,1423617] 4 64320cc3 [0,-1,0,-295265,-60683775] 2 64320cc4 [0,-1,0,-517985,143599617] 2
64320cd (4 curves)	0	2- 3+ 5- 67-	2- 3+ 5-  0 -4  2 -6  4
Curve Equation t 64320cd1 [0,-1,0,2115,-538083] 2 64320cd2 [0,-1,0,-87665,-9641775] 4 64320cd3 [0,-1,0,-221665,27047425] 2 64320cd4 [0,-1,0,-1390145,-630403743] 2
64320ce (2 curves)	2	2- 3+ 5- 67-	2- 3+ 5- -2  0 -2  0 -4
Curve Equation t Generators 64320ce1 [0,-1,0,-2425,46777] 2 [27:16:1]&[-16:285:1] 64320ce2 [0,-1,0,-2625,38817] 2 [-3:216:1]&[7:144:1]
64320cf (4 curves)	1	2- 3- 5+ 67+	2- 3- 5+  0  4  2  2  0
Curve Equation t Generators 64320cf1 [0,1,0,-1676,-17730] 2 [2667:24002:27] 64320cf2 [0,1,0,-24121,-1449721] 4 [395:7128:1] 64320cf3 [0,1,0,-21441,-1781505] 2 [231:2376:1] 64320cf4 [0,1,0,-385921,-92406241] 2 [730:3927:1]
64320cg (1 curve)	1	2- 3- 5+ 67+	2- 3- 5+  1  3 -2 -2  6
Curve Equation t Generators 64320cg1 [0,1,0,-321,3519] 1 [15:48:1]
64320ch (1 curve)	1	2- 3- 5+ 67+	2- 3- 5+  2  0  4 -3  1
Curve Equation t Generators 64320ch1 [0,1,0,1709,46259] 1 [314:5625:1]
64320ci (2 curves)	1	2- 3- 5+ 67+	2- 3- 5+  2 -4  0  2 -4
Curve Equation t Generators 64320ci1 [0,1,0,-17441,619359] 2 [-11:900:1] 64320ci2 [0,1,0,46559,4164959] 2 [-25:1728:1]
64320cj (2 curves)	1	2- 3- 5+ 67+	2- 3- 5+ -4  2 -6 -4 -4
Curve Equation t Generators 64320cj1 [0,1,0,-32321,2330559] 2 [-155:1908:1] 64320cj2 [0,1,0,-523841,145756095] 2 [6447:514560:1]
64320ck (2 curves)	1	2- 3- 5+ 67+	2- 3- 5+ -4  6  2  0 -4
Curve Equation t Generators 64320ck1 [0,1,0,159,-5985] 2 [21:84:1] 64320ck2 [0,1,0,-4161,-100161] 2 [-33:48:1]
64320cl (2 curves)	0	2- 3- 5+ 67-	2- 3- 5+  4  0  4  0 -4
Curve Equation t 64320cl1 [0,1,0,-241,1295] 2 64320cl2 [0,1,0,159,5535] 2
64320cm (2 curves)	0	2- 3- 5- 67+	2- 3- 5-  2  0 -2  0  4
Curve Equation t 64320cm1 [0,1,0,-2425,-46777] 2 64320cm2 [0,1,0,-2625,-38817] 2
64320cn (1 curve)	0	2- 3- 5- 67+	2- 3- 5-  2 -2 -2  5  1
Curve Equation t 64320cn1 [0,1,0,-85,-2317] 1
64320co (2 curves)	0	2- 3- 5- 67+	2- 3- 5-  2 -4  2  0 -8
Curve Equation t 64320co1 [0,1,0,-209025,-36354177] 2 64320co2 [0,1,0,-413825,46344063] 2
64320cp (2 curves)	0	2- 3- 5- 67+	2- 3- 5-  4  0  4 -4  4
Curve Equation t 64320cp1 [0,1,0,-1985,26175] 2 64320cp2 [0,1,0,4415,165695] 2
64320cq (4 curves)	0	2- 3- 5- 67+	2- 3- 5-  4 -4 -2 -6 -4
Curve Equation t 64320cq1 [0,1,0,-6705,209103] 2 64320cq2 [0,1,0,-6785,203775] 4 64320cq3 [0,1,0,3935,797663] 4 64320cq4 [0,1,0,-18785,-729825] 2
64320cr (4 curves)	0	2- 3- 5- 67+	2- 3- 5- -4  4 -2  2  4
Curve Equation t 64320cr1 [0,1,0,-4906145,4180805343] 2 64320cr2 [0,1,0,-5233825,3590129375] 4 64320cr3 [0,1,0,11918175,22213770975] 4 64320cr4 [0,1,0,-27628705,-52831531297] 2
64320cs (4 curves)	2	2- 3- 5- 67+	2- 3- 5- -4 -4 -6 -2 -4
Curve Equation t Generators 64320cs1 [0,1,0,-2545,48143] 2 [-49:240:1]&[-19:300:1] 64320cs2 [0,1,0,-4545,-40257] 4 [-57:192:1]&[-54:225:1] 64320cs3 [0,1,0,17055,-295137] 2 [33:552:1]&[42:705:1] 64320cs4 [0,1,0,-58145,-5410977] 2 [-137:48:1]&[298:1953:1]
64320ct (2 curves)	1	2- 3- 5- 67-	2- 3- 5-  2  0 -6  0  0
Curve Equation t Generators 64320ct1 [0,1,0,-195425,33186975] 2 [223:864:1] 64320ct2 [0,1,0,-196225,32900735] 2 [218:729:1]
64320cu (2 curves)	1	2- 3- 5- 67-	2- 3- 5-  2  4  2  4 -4
Curve Equation t Generators 64320cu1 [0,1,0,-2745,51975] 2 [-15:300:1] 64320cu2 [0,1,0,-7745,-197025] 2 [-35:180:1]
64320cv (4 curves)	1	2- 3- 5- 67-	2- 3- 5- -2  0 -2  0  8
Curve Equation t Generators 64320cv1 [0,1,0,-57025,-4522177] 2 [-134:855:1] 64320cv2 [0,1,0,-876225,-315982017] 2 [-392598:703:729] 64320cv3 [0,1,0,-1224385,520531775] 2 [610:1005:1] 64320cv4 [0,1,0,-1544385,226835775] 2 [5925:446220:1]
64320cw (2 curves)	1	2- 3- 5- 67-	2- 3- 5- -2 -6 -2 -3 -1
Curve Equation t Generators 64320cw1 [0,1,0,955,-1407] 1 [16:135:1] 64320cw2 [0,1,0,-12005,555225] 1 [-80:1005:1]
64320cx (1 curve)	1	2- 3- 5- 67-	2- 3- 5- -3  3  6 -6  2
Curve Equation t Generators 64320cx1 [0,1,0,2975,17375] 1 [95:-1080:1]

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

Part of Computational Number Theory
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