Cremona's table of elliptic curves

99008 = 2⁶ · 7 · 13 · 17

Class	r	Atkin-Lehner	Eigenvalues
99008a (2 curves)	1	2+ 7+ 13+ 17+	2+  0 -2 7+  2 13+ 17+  4
Curve Equation t Generators 99008a1 [0,0,0,-1076,-13536] 2 [-19:7:1] 99008a2 [0,0,0,-556,-26640] 2 [85:735:1]
99008b (1 curve)	1	2+ 7+ 13+ 17+	2+  0 -3 7+  4 13+ 17+  1
Curve Equation t Generators 99008b1 [0,0,0,88006,-474304626] 1 [921439964388179043:117893855871133894923:56300788871783]
99008c (1 curve)	1	2+ 7+ 13+ 17+	2+ -1 -2 7+  3 13+ 17+  5
Curve Equation t Generators 99008c1 [0,-1,0,751,8593] 1 [-9:32:1]
99008d (2 curves)	1	2+ 7+ 13+ 17+	2+ -2 -2 7+  4 13+ 17+  2
Curve Equation t Generators 99008d1 [0,1,0,-229,651] 2 [-13:40:1] 99008d2 [0,1,0,751,5551] 2 [10:119:1]
99008e (4 curves)	0	2+ 7+ 13+ 17-	2+  0 -2 7+ -4 13+ 17-  4
Curve Equation t 99008e1 [0,0,0,-58796,-5139664] 2 99008e2 [0,0,0,-924076,-341906640] 4 99008e3 [0,0,0,-907436,-354812624] 2 99008e4 [0,0,0,-14785196,-21882087120] 2
99008f (2 curves)	0	2+ 7+ 13+ 17-	2+  2  0 7+  4 13+ 17-  4
Curve Equation t 99008f1 [0,-1,0,-13588,-607770] 2 99008f2 [0,-1,0,-217673,-39016567] 2
99008g (2 curves)	0	2+ 7+ 13+ 17-	2+  2  0 7+  4 13+ 17- -4
Curve Equation t 99008g1 [0,-1,0,-833,833] 2 99008g2 [0,-1,0,3327,3329] 2
99008h (1 curve)	0	2+ 7+ 13+ 17-	2+  2 -1 7+  0 13+ 17-  5
Curve Equation t 99008h1 [0,-1,0,-25575542021,1574300868678557] 1
99008i (1 curve)	0	2+ 7+ 13+ 17-	2+  2 -1 7+  0 13+ 17- -6
Curve Equation t 99008i1 [0,-1,0,-3161020801,-68404150612863] 1
99008j (2 curves)	0	2+ 7+ 13+ 17-	2+  2  4 7+  0 13+ 17-  4
Curve Equation t 99008j1 [0,-1,0,-1041,13073] 2 99008j2 [0,-1,0,-1,36993] 2
99008k (1 curve)	0	2+ 7+ 13+ 17-	2+ -3  4 7+ -1 13+ 17-  1
Curve Equation t 99008k1 [0,0,0,-25765648,-50757231320] 1
99008l (1 curve)	0	2+ 7+ 13+ 17-	2+ -3  4 7+ -5 13+ 17- -5
Curve Equation t 99008l1 [0,0,0,-102028,-13596560] 1
99008m (1 curve)	0	2+ 7+ 13- 17+	2+ -1  0 7+ -1 13- 17+  1
Curve Equation t 99008m1 [0,-1,0,-92513,10967521] 1
99008n (1 curve)	0	2+ 7+ 13- 17+	2+ -1  0 7+ -5 13- 17+  1
Curve Equation t 99008n1 [0,-1,0,-33,-479] 1
99008o (2 curves)	0	2+ 7+ 13- 17+	2+  2 -4 7+  6 13- 17+  4
Curve Equation t 99008o1 [0,-1,0,-56225,-5095519] 2 99008o2 [0,-1,0,-83265,339521] 2
99008p (1 curve)	0	2+ 7+ 13- 17+	2+ -2 -3 7+ -4 13- 17+ -6
Curve Equation t 99008p1 [0,1,0,2687743,-563781281] 1
99008q (1 curve)	1	2+ 7+ 13- 17-	2+ -1 -4 7+  3 13- 17-  1
Curve Equation t Generators 99008q1 [0,-1,0,-5,-59] 1 [5:4:1]
99008r (2 curves)	2	2+ 7- 13+ 17+	2+  0 -2 7- -2 13+ 17+ -4
Curve Equation t Generators 99008r1 [0,0,0,-1076,13536] 2 [-34:104:1]&[5:91:1] 99008r2 [0,0,0,-556,26640] 2 [-32:108:1]&[-22:168:1]
99008s (1 curve)	0	2+ 7- 13+ 17+	2+  0 -3 7- -4 13+ 17+ -1
Curve Equation t 99008s1 [0,0,0,88006,474304626] 1
99008t (1 curve)	0	2+ 7- 13+ 17+	2+  1 -2 7-  1 13+ 17+ -5
Curve Equation t 99008t1 [0,1,0,-11149,-456845] 1
99008u (2 curves)	2	2+ 7- 13+ 17+	2+ -1  0 7- -3 13+ 17+  1
Curve Equation t Generators 99008u1 [0,-1,0,-133,773] 1 [-11:28:1]&[-4:35:1] 99008u2 [0,-1,0,987,-6395] 1 [9:56:1]&[13:92:1]
99008v (2 curves)	0	2+ 7- 13+ 17+	2+ -1  0 7- -3 13+ 17+  7
Curve Equation t 99008v1 [0,-1,0,-2913,66529] 1 99008v2 [0,-1,0,17887,-60767] 1
99008w (1 curve)	0	2+ 7- 13+ 17+	2+ -1  2 7- -3 13+ 17+  0
Curve Equation t 99008w1 [0,-1,0,-3297,-6205343] 1
99008x (3 curves)	0	2+ 7- 13+ 17+	2+  2 -3 7-  0 13+ 17+ -2
Curve Equation t 99008x1 [0,-1,0,-22337,1292609] 1 99008x2 [0,-1,0,5823,4234049] 1 99008x3 [0,-1,0,-52417,-114517311] 1
99008y (2 curves)	2	2+ 7- 13+ 17+	2+ -2  0 7- -2 13+ 17+ -8
Curve Equation t Generators 99008y1 [0,1,0,-2913,-8321] 2 [-37:224:1]&[-35:228:1] 99008y2 [0,1,0,-29953,1976415] 2 [-133:1904:1]&[-14:1547:1]
99008z (1 curve)	1	2+ 7- 13+ 17-	2+  1  2 7-  1 13+ 17-  5
Curve Equation t Generators 99008z1 [0,1,0,-497,-6097] 1 [939:3808:27]
99008ba (2 curves)	1	2+ 7- 13+ 17-	2+ -1  0 7- -3 13+ 17-  7
Curve Equation t Generators 99008ba1 [0,-1,0,-14693,690469] 1 [101:476:1] 99008ba2 [0,-1,0,-1093,1890533] 1 [29:1372:1]
99008bb (4 curves)	1	2+ 7- 13+ 17-	2+  2  0 7-  0 13+ 17-  4
Curve Equation t Generators 99008bb1 [0,-1,0,-303233,63580289] 2 [451:4284:1] 99008bb2 [0,-1,0,-36993,171088001] 2 [800:25551:1] 99008bb3 [0,-1,0,-2479233,-1470186367] 2 [46019:9866052:1] 99008bb4 [0,-1,0,332927,-4618118271] 2 [164777565915:35345091890276:3581577]
99008bc (2 curves)	1	2+ 7- 13+ 17-	2+ -2  0 7- -4 13+ 17- -4
Curve Equation t Generators 99008bc1 [0,1,0,-13588,607770] 2 [61:98:1] 99008bc2 [0,1,0,-217673,39016567] 2 [271:-56:1]
99008bd (1 curve)	1	2+ 7- 13+ 17-	2+ -2 -3 7- -4 13+ 17- -2
Curve Equation t Generators 99008bd1 [0,1,0,-53537,-6089921] 1 [579:-12544:1]
99008be (2 curves)	1	2+ 7- 13- 17+	2+  0  2 7- -2 13- 17+  0
Curve Equation t Generators 99008be1 [0,0,0,-54284,4867952] 2 [-74:2912:1] 99008be2 [0,0,0,-52204,5258160] 2 [-72:2940:1]
99008bf (1 curve)	1	2+ 7- 13- 17+	2+  1  2 7- -1 13- 17+ -8
Curve Equation t Generators 99008bf1 [0,1,0,-8897,449183] 1 [77:476:1]
99008bg (1 curve)	1	2+ 7- 13- 17+	2+ -1  2 7- -3 13- 17+  7
Curve Equation t Generators 99008bg1 [0,-1,0,-17297,1030417] 1 [-57:1352:1]
99008bh (1 curve)	1	2+ 7- 13- 17+	2+  2  1 7-  0 13- 17+  3
Curve Equation t Generators 99008bh1 [0,-1,0,-105365,-17001907] 1 [79820:1656837:125]
99008bi (1 curve)	1	2+ 7- 13- 17+	2+  2 -1 7-  0 13- 17+ -2
Curve Equation t Generators 99008bi1 [0,-1,0,-161,-991] 1 [435:496:27]
99008bj (1 curve)	0	2+ 7- 13- 17-	2+  1  0 7- -3 13- 17-  5
Curve Equation t 99008bj1 [0,1,0,-82744513,289678040095] 1
99008bk (1 curve)	0	2+ 7- 13- 17-	2+  3  2 7-  5 13- 17-  5
Curve Equation t 99008bk1 [0,0,0,296,-122488] 1
99008bl (1 curve)	0	2+ 7- 13- 17-	2+ -3 -2 7-  3 13- 17- -4
Curve Equation t 99008bl1 [0,0,0,-1595116,-775647056] 1
99008bm (2 curves)	0	2- 7+ 13+ 17+	2-  1  0 7+  3 13+ 17+ -1
Curve Equation t 99008bm1 [0,1,0,-133,-773] 1 99008bm2 [0,1,0,987,6395] 1
99008bn (2 curves)	0	2- 7+ 13+ 17+	2-  1  0 7+  3 13+ 17+ -7
Curve Equation t 99008bn1 [0,1,0,-2913,-66529] 1 99008bn2 [0,1,0,17887,60767] 1
99008bo (1 curve)	0	2- 7+ 13+ 17+	2-  1  2 7+  3 13+ 17+  0
Curve Equation t 99008bo1 [0,1,0,-3297,6205343] 1
99008bp (1 curve)	0	2- 7+ 13+ 17+	2- -1  2 7+ -1 13+ 17+ -1
Curve Equation t 99008bp1 [0,-1,0,343,10633] 1
99008bq (1 curve)	0	2- 7+ 13+ 17+	2- -1  2 7+ -1 13+ 17+ -4
Curve Equation t 99008bq1 [0,-1,0,-1799617,-928619743] 1
99008br (1 curve)	2	2- 7+ 13+ 17+	2- -1 -2 7+ -1 13+ 17+  5
Curve Equation t Generators 99008br1 [0,-1,0,-11149,456845] 1 [61:4:1]&[193:2336:1]
99008bs (2 curves)	0	2- 7+ 13+ 17+	2-  2  0 7+  2 13+ 17+  8
Curve Equation t 99008bs1 [0,-1,0,-2913,8321] 2 99008bs2 [0,-1,0,-29953,-1976415] 2
99008bt (3 curves)	0	2- 7+ 13+ 17+	2- -2 -3 7+  0 13+ 17+  2
Curve Equation t 99008bt1 [0,1,0,-22337,-1292609] 1 99008bt2 [0,1,0,5823,-4234049] 1 99008bt3 [0,1,0,-52417,114517311] 1
99008bu (2 curves)	0	2- 7+ 13+ 17+	2- -2 -4 7+  2 13+ 17+  4
Curve Equation t 99008bu1 [0,1,0,-397145,-86260121] 2 99008bu2 [0,1,0,-1539585,643759039] 2
99008bv (1 curve)	1	2- 7+ 13+ 17-	2-  0  1 7+  0 13+ 17-  5
Curve Equation t Generators 99008bv1 [0,0,0,-62,198] 1 [-7:17:1]
99008bw (4 curves)	1	2- 7+ 13+ 17-	2-  0  2 7+  0 13+ 17-  0
Curve Equation t Generators 99008bw1 [0,0,0,9361,-1260880] 2 [136611440:1059530865:1404928] 99008bw2 [0,0,0,-133444,-17255040] 4 [-85344:252960:343] 99008bw3 [0,0,0,-464684,102388848] 4 [1604:59024:1] 99008bw4 [0,0,0,-2087084,-1160525168] 2 [12122674680:-991865794087:1728000]
99008bx (2 curves)	1	2- 7+ 13+ 17-	2-  1  0 7+  3 13+ 17- -7
Curve Equation t Generators 99008bx1 [0,1,0,-14693,-690469] 1 [8085:126208:27] 99008bx2 [0,1,0,-1093,-1890533] 1 [7194353133:117563145472:24642171]
99008by (1 curve)	1	2- 7+ 13+ 17-	2- -1  2 7+ -1 13+ 17- -5
Curve Equation t Generators 99008by1 [0,-1,0,-497,6097] 1 [3:68:1]
99008bz (1 curve)	1	2- 7+ 13+ 17-	2-  2 -3 7+  4 13+ 17-  2
Curve Equation t Generators 99008bz1 [0,-1,0,-53537,6089921] 1 [2749:143616:1]
99008ca (4 curves)	1	2- 7+ 13+ 17-	2- -2  0 7+  0 13+ 17- -4
Curve Equation t Generators 99008ca1 [0,1,0,-303233,-63580289] 2 [-315:884:1] 99008ca2 [0,1,0,-36993,-171088001] 2 [1410:50813:1] 99008ca3 [0,1,0,-2479233,1470186367] 2 [1951:63744:1] 99008ca4 [0,1,0,332927,4618118271] 2 [39495:2450492:27]
99008cb (1 curve)	1	2- 7+ 13+ 17-	2- -2 -1 7+ -4 13+ 17- -2
Curve Equation t Generators 99008cb1 [0,1,0,-1,5823] 1 [23:136:1]
99008cc (1 curve)	1	2- 7+ 13+ 17-	2-  3  2 7+  3 13+ 17- -3
Curve Equation t Generators 99008cc1 [0,0,0,-244,1472] 1 [228:100:27]
99008cd (2 curves)	1	2- 7+ 13- 17+	2-  0  2 7+  2 13- 17+  0
Curve Equation t Generators 99008cd1 [0,0,0,-54284,-4867952] 2 [1434:53536:1] 99008cd2 [0,0,0,-52204,-5258160] 2 [491771:18365955:343]
99008ce (1 curve)	1	2- 7+ 13- 17+	2-  1  2 7+  3 13- 17+ -7
Curve Equation t Generators 99008ce1 [0,1,0,-17297,-1030417] 1 [317:5044:1]
99008cf (1 curve)	1	2- 7+ 13- 17+	2- -1  2 7+  1 13- 17+  8
Curve Equation t Generators 99008cf1 [0,-1,0,-8897,-449183] 1 [42609:202096:343]
99008cg (1 curve)	1	2- 7+ 13- 17+	2- -2  1 7+  0 13- 17+ -3
Curve Equation t Generators 99008cg1 [0,1,0,-105365,17001907] 1 [-338:3757:1]
99008ch (1 curve)	1	2- 7+ 13- 17+	2- -2 -1 7+  0 13- 17+  2
Curve Equation t Generators 99008ch1 [0,1,0,-161,991] 1 [7:-16:1]
99008ci (1 curve)	1	2- 7+ 13- 17+	2- -3  2 7+ -3 13- 17+ -4
Curve Equation t Generators 99008ci1 [0,0,0,116,-1328] 1 [16:68:1]
99008cj (1 curve)	0	2- 7+ 13- 17-	2- -1  0 7+  3 13- 17- -5
Curve Equation t 99008cj1 [0,-1,0,-82744513,-289678040095] 1
99008ck (1 curve)	0	2- 7+ 13- 17-	2-  3 -2 7+ -3 13- 17-  4
Curve Equation t 99008ck1 [0,0,0,-1595116,775647056] 1
99008cl (1 curve)	2	2- 7+ 13- 17-	2- -3  2 7+ -5 13- 17- -5
Curve Equation t Generators 99008cl1 [0,0,0,296,122488] 1 [-31:289:1]&[-14:340:1]
99008cm (1 curve)	1	2- 7- 13+ 17+	2-  1  2 7-  1 13+ 17+  1
Curve Equation t Generators 99008cm1 [0,1,0,343,-10633] 1 [17:20:1]
99008cn (1 curve)	1	2- 7- 13+ 17+	2-  1  2 7-  1 13+ 17+  4
Curve Equation t Generators 99008cn1 [0,1,0,-1799617,928619743] 1 [777:136:1]
99008co (1 curve)	1	2- 7- 13+ 17+	2-  1 -2 7- -3 13+ 17+ -5
Curve Equation t Generators 99008co1 [0,1,0,751,-8593] 1 [29:196:1]
99008cp (2 curves)	1	2- 7- 13+ 17+	2-  2 -2 7- -4 13+ 17+ -2
Curve Equation t Generators 99008cp1 [0,-1,0,-229,-651] 2 [-12:15:1] 99008cp2 [0,-1,0,751,-5551] 2 [25:168:1]
99008cq (2 curves)	1	2- 7- 13+ 17+	2-  2 -4 7- -2 13+ 17+ -4
Curve Equation t Generators 99008cq1 [0,-1,0,-397145,86260121] 2 [475:2136:1] 99008cq2 [0,-1,0,-1539585,-643759039] 2 [-895:4056:1]
99008cr (1 curve)	0	2- 7- 13+ 17-	2-  0  1 7-  0 13+ 17- -5
Curve Equation t 99008cr1 [0,0,0,-62,-198] 1
99008cs (4 curves)	0	2- 7- 13+ 17-	2-  0  2 7-  0 13+ 17-  0
Curve Equation t 99008cs1 [0,0,0,9361,1260880] 2 99008cs2 [0,0,0,-133444,17255040] 4 99008cs3 [0,0,0,-464684,-102388848] 2 99008cs4 [0,0,0,-2087084,1160525168] 4
99008ct (4 curves)	2	2- 7- 13+ 17-	2-  0 -2 7-  4 13+ 17- -4
Curve Equation t Generators 99008ct1 [0,0,0,-58796,5139664] 2 [60:1352:1]&[300:3808:1] 99008ct2 [0,0,0,-924076,341906640] 4 [-1019:15015:1]&[437:4641:1] 99008ct3 [0,0,0,-907436,354812624] 2 [-758:24640:1]&[-275:24157:1] 99008ct4 [0,0,0,-14785196,21882087120] 2 [2229:735:1]&[29445:5011545:1]
99008cu (1 curve)	0	2- 7- 13+ 17-	2-  2 -1 7-  4 13+ 17-  2
Curve Equation t 99008cu1 [0,-1,0,-1,-5823] 1
99008cv (2 curves)	2	2- 7- 13+ 17-	2- -2  0 7- -4 13+ 17-  4
Curve Equation t Generators 99008cv1 [0,1,0,-833,-833] 2 [-27:52:1]&[-14:91:1] 99008cv2 [0,1,0,3327,-3329] 2 [5:116:1]&[15:224:1]
99008cw (1 curve)	0	2- 7- 13+ 17-	2- -2 -1 7-  0 13+ 17- -5
Curve Equation t 99008cw1 [0,1,0,-25575542021,-1574300868678557] 1
99008cx (1 curve)	0	2- 7- 13+ 17-	2- -2 -1 7-  0 13+ 17-  6
Curve Equation t 99008cx1 [0,1,0,-3161020801,68404150612863] 1
99008cy (2 curves)	0	2- 7- 13+ 17-	2- -2  4 7-  0 13+ 17- -4
Curve Equation t 99008cy1 [0,1,0,-1041,-13073] 2 99008cy2 [0,1,0,-1,-36993] 2
99008cz (1 curve)	0	2- 7- 13+ 17-	2-  3  4 7-  1 13+ 17- -1
Curve Equation t 99008cz1 [0,0,0,-25765648,50757231320] 1
99008da (1 curve)	0	2- 7- 13+ 17-	2-  3  4 7-  5 13+ 17-  5
Curve Equation t 99008da1 [0,0,0,-102028,13596560] 1
99008db (1 curve)	0	2- 7- 13+ 17-	2- -3  2 7- -3 13+ 17-  3
Curve Equation t 99008db1 [0,0,0,-244,-1472] 1
99008dc (1 curve)	0	2- 7- 13- 17+	2-  1  0 7-  1 13- 17+ -1
Curve Equation t 99008dc1 [0,1,0,-92513,-10967521] 1
99008dd (1 curve)	0	2- 7- 13- 17+	2-  1  0 7-  5 13- 17+ -1
Curve Equation t 99008dd1 [0,1,0,-33,479] 1
99008de (1 curve)	0	2- 7- 13- 17+	2-  2 -3 7-  4 13- 17+  6
Curve Equation t 99008de1 [0,-1,0,2687743,563781281] 1
99008df (2 curves)	2	2- 7- 13- 17+	2- -2 -4 7- -6 13- 17+ -4
Curve Equation t Generators 99008df1 [0,1,0,-56225,5095519] 2 [145:-112:1]&[-182:3055:1] 99008df2 [0,1,0,-83265,-339521] 2 [399:-5488:1]&[-273:1456:1]
99008dg (1 curve)	0	2- 7- 13- 17+	2-  3  2 7-  3 13- 17+  4
Curve Equation t 99008dg1 [0,0,0,116,1328] 1
99008dh (1 curve)	1	2- 7- 13- 17-	2-  1 -4 7- -3 13- 17- -1
Curve Equation t Generators 99008dh1 [0,1,0,-5,59] 1 [-1:8:1]

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