Cremona's table of elliptic curves

45990 = 2 · 3² · 5 · 7 · 73

Class	r	Atkin-Lehner	Eigenvalues
45990a (1 curve)	1	2+ 3+ 5+ 7+ 73+	2+ 3+ 5+ 7+  0  3  0  3
Curve Equation t Generators 45990a1 [1,-1,0,-105,-675] 1 [30:-165:1]
45990b (2 curves)	1	2+ 3+ 5+ 7+ 73+	2+ 3+ 5+ 7+ -2  2 -6 -6
Curve Equation t Generators 45990b1 [1,-1,0,-349665,-76003075] 2 [-261918:1425007:729] 45990b2 [1,-1,0,-980385,275812541] 2 [250:6679:1]
45990c (1 curve)	1	2+ 3+ 5+ 7+ 73+	2+ 3+ 5+ 7+  3 -3 -6 -6
Curve Equation t Generators 45990c1 [1,-1,0,30765,-334449] 1 [525:12399:1]
45990d (2 curves)	1	2+ 3+ 5+ 7+ 73+	2+ 3+ 5+ 7+  4  0  2 -2
Curve Equation t Generators 45990d1 [1,-1,0,-879810,-316936684] 2 [1353675827724845:-40233350115176102:871804955377] 45990d2 [1,-1,0,-603330,-519928300] 2 [112902643:3645906213:68921]
45990e (1 curve)	1	2+ 3+ 5+ 7- 73-	2+ 3+ 5+ 7- -2  2  7 -5
Curve Equation t Generators 45990e1 [1,-1,0,-120,576] 1 [0:24:1]
45990f (2 curves)	0	2+ 3+ 5- 7+ 73+	2+ 3+ 5- 7+ -4  2  0  6
Curve Equation t 45990f1 [1,-1,0,-11649,-481027] 2 45990f2 [1,-1,0,-11529,-491515] 2
45990g (1 curve)	0	2+ 3+ 5- 7+ 73+	2+ 3+ 5- 7+  6  2  5  1
Curve Equation t 45990g1 [1,-1,0,108022866,365700541140] 1
45990h (1 curve)	1	2+ 3+ 5- 7+ 73-	2+ 3+ 5- 7+  2 -6  1  3
Curve Equation t Generators 45990h1 [1,-1,0,-3654,-124540] 1 [496:10702:1]
45990i (1 curve)	1	2+ 3+ 5- 7- 73+	2+ 3+ 5- 7- -1  3  2 -2
Curve Equation t Generators 45990i1 [1,-1,0,21,133] 1 [-1:11:1]
45990j (2 curves)	1	2+ 3+ 5- 7- 73+	2+ 3+ 5- 7- -4 -4  2  6
Curve Equation t Generators 45990j1 [1,-1,0,-1149,10565] 2 [59:352:1] 45990j2 [1,-1,0,3171,68453] 2 [-1:256:1]
45990k (2 curves)	0	2+ 3+ 5- 7- 73-	2+ 3+ 5- 7- -2  6  6 -2
Curve Equation t 45990k1 [1,-1,0,-294,-1820] 2 45990k2 [1,-1,0,-4674,-121832] 2
45990l (2 curves)	0	2+ 3+ 5- 7- 73-	2+ 3+ 5- 7-  3 -1  6  2
Curve Equation t 45990l1 [1,-1,0,741,-77985] 3 45990l2 [1,-1,0,-117384,-15454360] 1
45990m (1 curve)	0	2+ 3- 5+ 7+ 73+	2+ 3- 5+ 7+ -2  4  1  7
Curve Equation t 45990m1 [1,-1,0,-49950,-8477784] 1
45990n (1 curve)	0	2+ 3- 5+ 7+ 73+	2+ 3- 5+ 7+  3 -1 -6  0
Curve Equation t 45990n1 [1,-1,0,-630,-16740] 1
45990o (2 curves)	0	2+ 3- 5+ 7+ 73+	2+ 3- 5+ 7+ -4 -4  0  4
Curve Equation t 45990o1 [1,-1,0,-513401805,-4477356779675] 2 45990o2 [1,-1,0,-512002125,-4502984640539] 2
45990p (1 curve)	0	2+ 3- 5+ 7+ 73+	2+ 3- 5+ 7+  6  6  0 -6
Curve Equation t 45990p1 [1,-1,0,-630,18036] 1
45990q (1 curve)	1	2+ 3- 5+ 7+ 73-	2+ 3- 5+ 7+  6 -2 -3  1
Curve Equation t Generators 45990q1 [1,-1,0,765,-43659] 1 [45:261:1]
45990r (1 curve)	1	2+ 3- 5+ 7+ 73-	2+ 3- 5+ 7+ -6  4 -3  5
Curve Equation t Generators 45990r1 [1,-1,0,9540,1193296] 1 [-40:884:1]
45990s (2 curves)	1	2+ 3- 5+ 7- 73+	2+ 3- 5+ 7-  6  2  4 -4
Curve Equation t Generators 45990s1 [1,-1,0,-701505,226319485] 2 [458:743:1] 45990s2 [1,-1,0,-675225,244037461] 2 [323:-7879:1]
45990t (1 curve)	0	2+ 3- 5+ 7- 73-	2+ 3- 5+ 7-  4 -4 -2 -2
Curve Equation t 45990t1 [1,-1,0,-315,-2079] 1
45990u (1 curve)	0	2+ 3- 5+ 7- 73-	2+ 3- 5+ 7-  4 -4 -5  1
Curve Equation t 45990u1 [1,-1,0,11970,-6863724] 1
45990v (6 curves)	0	2+ 3- 5+ 7- 73-	2+ 3- 5+ 7-  4  6  6  4
Curve Equation t 45990v1 [1,-1,0,-825480,-288446400] 2 45990v2 [1,-1,0,-883800,-245301264] 4 45990v3 [1,-1,0,2072700,-1538474364] 2 45990v4 [1,-1,0,-4773420,3808460700] 4 45990v5 [1,-1,0,3495330,15611274450] 2 45990v6 [1,-1,0,-75276090,251399737206] 2
45990w (1 curve)	1	2+ 3- 5- 7+ 73+	2+ 3- 5- 7+  2  2  3 -3
Curve Equation t Generators 45990w1 [1,-1,0,-17934,928988] 1 [67:124:1]
45990x (1 curve)	1	2+ 3- 5- 7+ 73+	2+ 3- 5- 7+  2  3  6  1
Curve Equation t Generators 45990x1 [1,-1,0,4221,-274347] 1 [198:2781:1]
45990y (4 curves)	1	2+ 3- 5- 7+ 73+	2+ 3- 5- 7+ -4  2 -6  4
Curve Equation t Generators 45990y1 [1,-1,0,2781,-159467] 2 [87:814:1] 45990y2 [1,-1,0,-32499,-2015195] 4 [-109:527:1] 45990y3 [1,-1,0,-124479,14780353] 2 [-208:5729:1] 45990y4 [1,-1,0,-504999,-138000695] 2 [-409:227:1]
45990z (4 curves)	0	2+ 3- 5- 7+ 73-	2+ 3- 5- 7+  0  2 -2  4
Curve Equation t 45990z1 [1,-1,0,-3821769,-2873167475] 2 45990z2 [1,-1,0,-4559049,-1685704307] 4 45990z3 [1,-1,0,16044471,-12716828915] 2 45990z4 [1,-1,0,-36959049,85334215693] 2
45990ba (1 curve)	0	2+ 3- 5- 7- 73+	2+ 3- 5- 7- -4  0  2 -2
Curve Equation t 45990ba1 [1,-1,0,-64764,-6368432] 1
45990bb (4 curves)	0	2+ 3- 5- 7- 73+	2+ 3- 5- 7- -4 -6  2  0
Curve Equation t 45990bb1 [1,-1,0,2961,-419027] 2 45990bb2 [1,-1,0,-69039,-6625427] 4 45990bb3 [1,-1,0,-200439,26198293] 2 45990bb4 [1,-1,0,-1089639,-437522747] 2
45990bc (4 curves)	1	2+ 3- 5- 7- 73-	2+ 3- 5- 7-  0 -6 -2 -4
Curve Equation t Generators 45990bc1 [1,-1,0,-32319,-964467] 2 [-98:1169:1] 45990bc2 [1,-1,0,-265599,52083405] 4 [-314:10377:1] 45990bc3 [1,-1,0,-29079,141346053] 2 [117:-11871:1] 45990bc4 [1,-1,0,-4234599,3355085205] 2 [1191:-438:1]
45990bd (1 curve)	1	2+ 3- 5- 7- 73-	2+ 3- 5- 7- -2  0  3  1
Curve Equation t Generators 45990bd1 [1,-1,0,347661,-68591255] 1 [1076:38837:1]
45990be (1 curve)	1	2+ 3- 5- 7- 73-	2+ 3- 5- 7- -3  1 -6  4
Curve Equation t Generators 45990be1 [1,-1,0,118026,-7656332] 1 [557:14909:1]
45990bf (4 curves)	1	2+ 3- 5- 7- 73-	2+ 3- 5- 7- -4  2  2  4
Curve Equation t Generators 45990bf1 [1,-1,0,-1449,-20867] 2 [59:281:1] 45990bf2 [1,-1,0,-1629,-15215] 4 [-16:89:1] 45990bf3 [1,-1,0,4941,-111137] 2 [47:449:1] 45990bf4 [1,-1,0,-11079,440275] 2 [89:347:1]
45990bg (2 curves)	0	2- 3+ 5+ 7+ 73+	2- 3+ 5+ 7+  4  2  0  6
Curve Equation t 45990bg1 [1,-1,1,-104843,13092571] 2 45990bg2 [1,-1,1,-103763,13374667] 2
45990bh (1 curve)	0	2- 3+ 5+ 7+ 73+	2- 3+ 5+ 7+ -6  2 -5  1
Curve Equation t 45990bh1 [1,-1,1,972205792,-9874886816573] 1
45990bi (1 curve)	1	2- 3+ 5+ 7+ 73-	2- 3+ 5+ 7+ -2 -6 -1  3
Curve Equation t Generators 45990bi1 [1,-1,1,-32888,3395467] 1 [-173:2057:1]
45990bj (1 curve)	1	2- 3+ 5+ 7- 73+	2- 3+ 5+ 7-  1  3 -2 -2
Curve Equation t Generators 45990bj1 [1,-1,1,187,-3779] 1 [13:20:1]
45990bk (2 curves)	1	2- 3+ 5+ 7- 73+	2- 3+ 5+ 7-  4 -4 -2  6
Curve Equation t Generators 45990bk1 [1,-1,1,-128,-349] 2 [-9:7:1] 45990bk2 [1,-1,1,352,-2653] 2 [25:-159:1]
45990bl (2 curves)	0	2- 3+ 5+ 7- 73-	2- 3+ 5+ 7-  2  6 -6 -2
Curve Equation t 45990bl1 [1,-1,1,-2648,51787] 2 45990bl2 [1,-1,1,-42068,3331531] 2
45990bm (2 curves)	0	2- 3+ 5+ 7- 73-	2- 3+ 5+ 7- -3 -1 -6  2
Curve Equation t 45990bm1 [1,-1,1,-13043,576731] 3 45990bm2 [1,-1,1,6667,2098927] 1
45990bn (1 curve)	1	2- 3+ 5- 7+ 73+	2- 3+ 5- 7+  0  3  0  3
Curve Equation t Generators 45990bn1 [1,-1,1,-947,19171] 1 [1:134:1]
45990bo (2 curves)	1	2- 3+ 5- 7+ 73+	2- 3+ 5- 7+  2  2  6 -6
Curve Equation t Generators 45990bo1 [1,-1,1,-38852,2827879] 2 [37:-1219:1] 45990bo2 [1,-1,1,-108932,-10178969] 2 [391:2429:1]
45990bp (1 curve)	1	2- 3+ 5- 7+ 73+	2- 3+ 5- 7+ -3 -3  6 -6
Curve Equation t Generators 45990bp1 [1,-1,1,276883,8753239] 1 [33214203933599656:-3223185414984154783:676466195106304]
45990bq (2 curves)	1	2- 3+ 5- 7+ 73+	2- 3+ 5- 7+ -4  0 -2 -2
Curve Equation t Generators 45990bq1 [1,-1,1,-97757,11770981] 2 [-209:4904:1] 45990bq2 [1,-1,1,-67037,19278949] 2 [107:3596:1]
45990br (1 curve)	1	2- 3+ 5- 7- 73-	2- 3+ 5- 7-  2  2 -7 -5
Curve Equation t Generators 45990br1 [1,-1,1,-1082,-14471] 1 [73:503:1]
45990bs (2 curves)	1	2- 3- 5+ 7+ 73+	2- 3- 5+ 7+  0 -4  0  0
Curve Equation t Generators 45990bs1 [1,-1,1,-413348,-102114169] 2 [-365:357:1] 45990bs2 [1,-1,1,-325868,-146623993] 2 [891:15979:1]
45990bt (1 curve)	1	2- 3- 5+ 7+ 73+	2- 3- 5+ 7+  2  3 -2  5
Curve Equation t Generators 45990bt1 [1,-1,1,5724333382,-275486116804243] 1 [66063339757458565184318639843177195922431871701053307059703039768067037188:-39355847566273245613826605573308040657790903279214013253005334975226112915637:194395743303729825159782145465060173467180094055952638676467068950336]
45990bu (1 curve)	1	2- 3- 5+ 7+ 73+	2- 3- 5+ 7+  2 -4  5  5
Curve Equation t Generators 45990bu1 [1,-1,1,-64418,8912801] 1 [-159:3967:1]
45990bv (1 curve)	1	2- 3- 5+ 7+ 73+	2- 3- 5+ 7+  2  6 -5 -7
Curve Equation t Generators 45990bv1 [1,-1,1,-279878,-63311659] 1 [753:11971:1]
45990bw (4 curves)	1	2- 3- 5+ 7+ 73+	2- 3- 5+ 7+ -4  2  2 -4
Curve Equation t Generators 45990bw1 [1,-1,1,-383,-8809] 2 [33:100:1] 45990bw2 [1,-1,1,-9203,-336913] 4 [1910:25613:8] 45990bw3 [1,-1,1,-12353,-83653] 2 [168264:2778719:512] 45990bw4 [1,-1,1,-147173,-21694669] 2 [3638:16533:8]
45990bx (2 curves)	1	2- 3- 5+ 7+ 73+	2- 3- 5+ 7+ -6 -2 -4 -8
Curve Equation t Generators 45990bx1 [1,-1,1,-330773,71353581] 2 [191:3792:1] 45990bx2 [1,-1,1,89707,240050157] 2 [83:-15792:1]
45990by (1 curve)	0	2- 3- 5+ 7+ 73-	2- 3- 5+ 7+  6  4  1 -1
Curve Equation t 45990by1 [1,-1,1,157,807] 1
45990bz (1 curve)	0	2- 3- 5+ 7- 73+	2- 3- 5+ 7-  1  5 -2  0
Curve Equation t 45990bz1 [1,-1,1,-383,3017] 1
45990ca (1 curve)	0	2- 3- 5+ 7- 73+	2- 3- 5+ 7-  4 -4  1 -3
Curve Equation t 45990ca1 [1,-1,1,-2741513,-1746477943] 1
45990cb (3 curves)	1	2- 3- 5+ 7- 73-	2- 3- 5+ 7-  0 -4  6  2
Curve Equation t Generators 45990cb1 [1,-1,1,3442,25481] 1 [72693:811189:729] 45990cb2 [1,-1,1,-58433,5614481] 3 [133:360:1] 45990cb3 [1,-1,1,-4772408,4014056891] 3 [10666543:123252099:6859]
45990cc (4 curves)	1	2- 3- 5+ 7- 73-	2- 3- 5+ 7- -4 -2 -2  0
Curve Equation t Generators 45990cc1 [1,-1,1,-634568,194722827] 2 [455:-39:1] 45990cc2 [1,-1,1,-646088,187294731] 4 [995:-23493:1] 45990cc3 [1,-1,1,588712,817536651] 2 [603:-37605:1] 45990cc4 [1,-1,1,-2065208,-918483573] 2 [-513:2657:1]
45990cd (1 curve)	0	2- 3- 5- 7+ 73+	2- 3- 5- 7+  2  0  3 -1
Curve Equation t 45990cd1 [1,-1,1,-742712,-246181701] 1
45990ce (1 curve)	1	2- 3- 5- 7+ 73-	2- 3- 5- 7+ -2  2  4  6
Curve Equation t Generators 45990ce1 [1,-1,1,178,1549] 1 [-1:37:1]
45990cf (1 curve)	1	2- 3- 5- 7+ 73-	2- 3- 5- 7+  3 -5 -2 -4
Curve Equation t Generators 45990cf1 [1,-1,1,-21452,1232079] 1 [77:141:1]
45990cg (4 curves)	1	2- 3- 5- 7+ 73-	2- 3- 5- 7+  4 -2 -2 -4
Curve Equation t Generators 45990cg1 [1,-1,1,6988,208919] 4 [9:517:1] 45990cg2 [1,-1,1,-39092,1978391] 4 [-129:2269:1] 45990cg3 [1,-1,1,-250772,-46792681] 2 [-311:1177:1] 45990cg4 [1,-1,1,-564692,163442711] 2 [459:661:1]
45990ch (1 curve)	1	2- 3- 5- 7+ 73-	2- 3- 5- 7+ -6 -2  1  5
Curve Equation t Generators 45990ch1 [1,-1,1,-7192742,8553033141] 1 [1061:-46521:1]
45990ci (1 curve)	1	2- 3- 5- 7- 73+	2- 3- 5- 7-  2 -5  2 -5
Curve Equation t Generators 45990ci1 [1,-1,1,1948,-94521] 1 [47:291:1]
45990cj (2 curves)	0	2- 3- 5- 7- 73-	2- 3- 5- 7-  6 -7  6 -7
Curve Equation t 45990cj1 [1,-1,1,-16412,-854989] 1 45990cj2 [1,-1,1,94153,-671281] 3

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