Cremona's table of elliptic curves

41616 = 2⁴ · 3² · 17²

Class	r	Atkin-Lehner	Eigenvalues
41616a (1 curve)	1	2+ 3+ 17+	2+ 3+  1 -2  3 -1 17+  3
Curve Equation t Generators 41616a1 [0,0,0,3468,-19652] 1 [153:2023:1]
41616b (1 curve)	1	2+ 3+ 17+	2+ 3+ -1 -2 -3 -1 17+  3
Curve Equation t Generators 41616b1 [0,0,0,31212,530604] 1 [-15:243:1]
41616c (1 curve)	1	2+ 3+ 17+	2+ 3+  2 -5 -6  5 17+ -3
Curve Equation t Generators 41616c1 [0,0,0,-57834,-5353317] 1 [874953078:110471961213:54872]
41616d (1 curve)	1	2+ 3+ 17+	2+ 3+ -2 -5  6  5 17+ -3
Curve Equation t Generators 41616d1 [0,0,0,-6426,198271] 1 [370:3:8]
41616e (1 curve)	1	2+ 3+ 17+	2+ 3+  3  0  1  0 17+  2
Curve Equation t Generators 41616e1 [0,0,0,-51,-238] 1 [13:36:1]
41616f (1 curve)	1	2+ 3+ 17+	2+ 3+  3  4  1 -5 17+ -5
Curve Equation t Generators 41616f1 [0,0,0,-1836,31212] 1 [33:81:1]
41616g (1 curve)	1	2+ 3+ 17+	2+ 3+  3 -4  1 -5 17+ -5
Curve Equation t Generators 41616g1 [0,0,0,-58956,-5679428] 1 [87445:2148513:125]
41616h (1 curve)	1	2+ 3+ 17+	2+ 3+ -3  0 -1  0 17+  2
Curve Equation t Generators 41616h1 [0,0,0,-459,6426] 1 [15:54:1]
41616i (1 curve)	1	2+ 3+ 17+	2+ 3+ -3  4 -1 -5 17+ -5
Curve Equation t Generators 41616i1 [0,0,0,-204,-1156] 1 [17:17:1]
41616j (1 curve)	1	2+ 3+ 17+	2+ 3+ -3 -4 -1 -5 17+ -5
Curve Equation t Generators 41616j1 [0,0,0,-530604,153344556] 1 [289:4913:1]
41616k (1 curve)	0	2+ 3+ 17-	2+ 3+  2  5 -6  5 17- -3
Curve Equation t 41616k1 [0,0,0,-1857114,974105423] 1
41616l (1 curve)	0	2+ 3+ 17-	2+ 3+ -2  5  6  5 17- -3
Curve Equation t 41616l1 [0,0,0,-16714026,-26300846421] 1
41616m (1 curve)	0	2+ 3+ 17-	2+ 3+  3  0  1  0 17-  2
Curve Equation t 41616m1 [0,0,0,-132651,31570938] 1
41616n (1 curve)	0	2+ 3+ 17-	2+ 3+ -3  0 -1  0 17-  2
Curve Equation t 41616n1 [0,0,0,-14739,-1169294] 1
41616o (2 curves)	2	2+ 3- 17+	2+ 3-  0  0 -2 -6 17+ -4
Curve Equation t Generators 41616o1 [0,0,0,-21675,-894166] 2 [-85:578:1]&[331:5310:1] 41616o2 [0,0,0,-125715,16438898] 2 [-203:5796:1]&[-187:5780:1]
41616p (1 curve)	2	2+ 3- 17+	2+ 3-  0 -1 -4 -5 17+ -5
Curve Equation t Generators 41616p1 [0,0,0,-3315,73474] 1 [33:-4:1]&[-19:360:1]
41616q (1 curve)	0	2+ 3- 17+	2+ 3-  0 -1  6  5 17+  5
Curve Equation t 41616q1 [0,0,0,-2505630,-3460191509] 1
41616r (2 curves)	0	2+ 3- 17+	2+ 3-  0  2  0  2 17+ -4
Curve Equation t 41616r1 [0,0,0,-125715,-16969502] 2 41616r2 [0,0,0,-21675,-44207174] 2
41616s (2 curves)	0	2+ 3- 17+	2+ 3-  0  2 -2 -2 17+  4
Curve Equation t 41616s1 [0,0,0,-255,-578] 2 41616s2 [0,0,0,-3315,-73406] 2
41616t (2 curves)	0	2+ 3- 17+	2+ 3-  0 -2  2 -2 17+  4
Curve Equation t 41616t1 [0,0,0,-73695,-2839714] 2 41616t2 [0,0,0,-958035,-360643678] 2
41616u (1 curve)	2	2+ 3- 17+	2+ 3-  0 -3 -2 -3 17+ -1
Curve Equation t Generators 41616u1 [0,0,0,-255,2414] 1 [-19:20:1]&[-2:54:1]
41616v (1 curve)	0	2+ 3- 17+	2+ 3-  1  4 -3  2 17+  0
Curve Equation t 41616v1 [0,0,0,-12277587,16564051762] 1
41616w (4 curves)	0	2+ 3- 17+	2+ 3-  2 -4 -4  6 17+ -4
Curve Equation t 41616w1 [0,0,0,-136119,19288438] 2 41616w2 [0,0,0,-188139,3193450] 4 41616w3 [0,0,0,748221,25478818] 2 41616w4 [0,0,0,-1956819,-1049171150] 2
41616x (6 curves)	0	2+ 3- 17+	2+ 3- -2  0 -4 -2 17+  4
Curve Equation t 41616x1 [0,0,0,1734,34391] 2 41616x2 [0,0,0,-11271,343910] 4 41616x3 [0,0,0,-63291,-5846470] 4 41616x4 [0,0,0,-167331,26343506] 2 41616x5 [0,0,0,40749,-23179534] 2 41616x6 [0,0,0,-999651,-384697726] 2
41616y (2 curves)	0	2+ 3- 17+	2+ 3- -2 -2  6  2 17+  0
Curve Equation t 41616y1 [0,0,0,-11271,186694] 2 41616y2 [0,0,0,40749,1424770] 2
41616z (1 curve)	0	2+ 3- 17+	2+ 3-  3  0  1  3 17+ -1
Curve Equation t 41616z1 [0,0,0,1328244,-229319188] 1
41616ba (1 curve)	2	2+ 3- 17+	2+ 3- -3 -4 -1 -5 17+  7
Curve Equation t Generators 41616ba1 [0,0,0,-45084,7526716] 1 [17:2601:1]&[185:2349:1]
41616bb (1 curve)	0	2+ 3- 17+	2+ 3-  4 -5  0 -1 17+  3
Curve Equation t 41616bb1 [0,0,0,357,-99110] 1
41616bc (1 curve)	0	2+ 3- 17+	2+ 3- -4 -1  2 -3 17+  5
Curve Equation t 41616bc1 [0,0,0,-102,-425] 1
41616bd (1 curve)	1	2+ 3- 17-	2+ 3-  0  1  4 -5 17- -5
Curve Equation t Generators 41616bd1 [0,0,0,-958035,360977762] 1 [289:10404:1]
41616be (1 curve)	1	2+ 3- 17-	2+ 3-  0  1 -6  5 17-  5
Curve Equation t Generators 41616be1 [0,0,0,-8670,-704293] 1 [486206:5001669:2744]
41616bf (1 curve)	1	2+ 3- 17-	2+ 3-  0  3  2 -3 17- -1
Curve Equation t Generators 41616bf1 [0,0,0,-73695,11859982] 1 [189:2164:1]
41616bg (1 curve)	1	2+ 3- 17-	2+ 3- -1 -4  3  2 17-  0
Curve Equation t Generators 41616bg1 [0,0,0,-42483,3371474] 1 [85:612:1]
41616bh (1 curve)	1	2+ 3- 17-	2+ 3-  4  1 -2 -3 17-  5
Curve Equation t Generators 41616bh1 [0,0,0,-29478,-2088025] 1 [14450:611235:8]
41616bi (1 curve)	1	2+ 3- 17-	2+ 3- -4  5  0 -1 17-  3
Curve Equation t Generators 41616bi1 [0,0,0,103173,-486927430] 1 [14161:1685448:1]
41616bj (2 curves)	0	2- 3+ 17+	2- 3+  0 -1  0  5 17+  1
Curve Equation t 41616bj1 [0,0,0,0,-1419857] 1 41616bj2 [0,0,0,0,38336139] 1
41616bk (4 curves)	0	2- 3+ 17+	2- 3+  0 -4  0  2 17+ -8
Curve Equation t 41616bk1 [0,0,0,0,-4913] 2 41616bk2 [0,0,0,-4335,-108086] 2 41616bk3 [0,0,0,0,132651] 2 41616bk4 [0,0,0,-39015,2918322] 2
41616bl (2 curves)	0	2- 3+ 17+	2- 3+  0  5  0 -7 17+  7
Curve Equation t 41616bl1 [0,0,0,0,-17] 1 41616bl2 [0,0,0,0,459] 1
41616bm (1 curve)	2	2- 3+ 17+	2- 3+  1 -2 -3 -5 17+  1
Curve Equation t Generators 41616bm1 [0,0,0,-13872,-707472] 1 [153:867:1]&[1513:58667:1]
41616bn (1 curve)	0	2- 3+ 17+	2- 3+ -1 -2  3 -5 17+  1
Curve Equation t 41616bn1 [0,0,0,-124848,19101744] 1
41616bo (1 curve)	0	2- 3+ 17+	2- 3+  2  1  6  1 17+ -5
Curve Equation t 41616bo1 [0,0,0,-459,-8262] 1
41616bp (1 curve)	2	2- 3+ 17+	2- 3+ -2  1 -6  1 17+ -5
Curve Equation t Generators 41616bp1 [0,0,0,-51,306] 1 [-9:6:1]&[9:24:1]
41616bq (2 curves)	0	2- 3+ 17+	2- 3+  3  2 -3 -1 17+  7
Curve Equation t 41616bq1 [0,0,0,-6936,1395292] 1 41616bq2 [0,0,0,-1186056,497175948] 1
41616br (2 curves)	0	2- 3+ 17+	2- 3+ -3  2  3 -1 17+  7
Curve Equation t 41616br1 [0,0,0,-131784,-18413924] 1 41616br2 [0,0,0,-62424,-37672884] 1
41616bs (2 curves)	1	2- 3+ 17-	2- 3+  0  1  0  5 17-  1
Curve Equation t Generators 41616bs1 [0,0,0,0,-289] 1 [17:68:1] 41616bs2 [0,0,0,0,7803] 1 [13:100:1]
41616bt (2 curves)	1	2- 3+ 17-	2- 3+  0 -5  0 -7 17-  7
Curve Equation t Generators 41616bt1 [0,0,0,0,-83521] 1 [578:4335:8] 41616bt2 [0,0,0,0,2255067] 1 [66:12015:8]
41616bu (1 curve)	1	2- 3+ 17-	2- 3+  2 -1  6  1 17- -5
Curve Equation t Generators 41616bu1 [0,0,0,-14739,1503378] 1 [289:4624:1]
41616bv (1 curve)	1	2- 3+ 17-	2- 3+ -2 -1 -6  1 17- -5
Curve Equation t Generators 41616bv1 [0,0,0,-132651,-40591206] 1 [477:2160:1]
41616bw (2 curves)	1	2- 3- 17+	2- 3-  0 -1  0 -1 17+  7
Curve Equation t Generators 41616bw1 [0,0,0,2805,13498] 1 [101:1152:1] 41616bw2 [0,0,0,-33915,-2711126] 1 [77483:368640:343]
41616bx (4 curves)	1	2- 3- 17+	2- 3-  0  2  0  2 17+  4
Curve Equation t Generators 41616bx1 [0,0,0,-10633755,13341870538] 2 [16847:2148426:1] 41616bx2 [0,0,0,-8969115,17660279626] 2 [5770905:-738001382:343] 41616bx3 [0,0,0,-31233675,-50795418566] 2 [-4372465280799:-185758275522560:1485446221] 41616bx4 [0,0,0,75303285,-322102440902] 2 [72475991803866421995:-10108217043494686388714:4528568485496125]
41616by (2 curves)	1	2- 3- 17+	2- 3-  0  4  4  2 17+ -4
Curve Equation t Generators 41616by1 [0,0,0,-3315,51442] 2 [-1:234:1] 41616by2 [0,0,0,8925,342754] 2 [135:2002:1]
41616bz (2 curves)	1	2- 3- 17+	2- 3-  0 -4 -4  2 17+ -4
Curve Equation t Generators 41616bz1 [0,0,0,-958035,252734546] 2 [-161:20070:1] 41616bz2 [0,0,0,2579325,1683950402] 2 [176395:-11273542:125]
41616ca (4 curves)	1	2- 3- 17+	2- 3-  0 -4 -6  2 17+  4
Curve Equation t Generators 41616ca1 [0,0,0,-125715,10621906] 2 [-238:5202:1] 41616ca2 [0,0,0,-1790355,921845842] 2 [1938:68782:1] 41616ca3 [0,0,0,-4287315,-3416372462] 2 [-2602054:442170:2197] 41616ca4 [0,0,0,-4703475,-2713145294] 2 [684660210:-8925221102:274625]
41616cb (1 curve)	1	2- 3- 17+	2- 3-  1  0 -5 -5 17+ -1
Curve Equation t Generators 41616cb1 [0,0,0,-13872,-962948] 1 [221:2601:1]
41616cc (1 curve)	1	2- 3- 17+	2- 3-  1 -2  3  3 17+  3
Curve Equation t Generators 41616cc1 [0,0,0,-117912,335086252] 1 [-8092:1193859:64]
41616cd (1 curve)	1	2- 3- 17+	2- 3- -1  2 -3  3 17+  3
Curve Equation t Generators 41616cd1 [0,0,0,-408,68204] 1 [34:306:1]
41616ce (1 curve)	1	2- 3- 17+	2- 3- -1  4  3  6 17+ -4
Curve Equation t Generators 41616ce1 [0,0,0,357,-27574] 1 [253:4032:1]
41616cf (1 curve)	1	2- 3- 17+	2- 3- -1  4 -3  3 17+ -1
Curve Equation t Generators 41616cf1 [0,0,0,-4217088,-3337951156] 1 [45429098810:-2683306569402:9938375]
41616cg (1 curve)	1	2- 3- 17+	2- 3-  2  1  0 -3 17+ -1
Curve Equation t Generators 41616cg1 [0,0,0,-2244,41123] 1 [242:243:8]
41616ch (4 curves)	1	2- 3- 17+	2- 3-  2  2  0 -6 17+  0
Curve Equation t Generators 41616ch1 [0,0,0,-7679019,7715502938] 2 [349025365:820787456:274625] 41616ch2 [0,0,0,-120874539,511503484250] 2 [726305:-9131616:125] 41616ch3 [0,0,0,-870794859,-9890573357158] 2 [-931753166465434645707445501491963061249415:78998573787993812907576043548299325462224:54728895109816609883782028800761339125] 41616ch4 [0,0,0,-877869579,-9721689886150] 2 [-709968674285157205873315:-22313686700722545357022872:43201614623047114625]
41616ci (6 curves)	1	2- 3- 17+	2- 3- -2  0  4 -2 17+ -4
Curve Equation t Generators 41616ci1 [0,0,0,-1415811,601361026] 2 [-1345:8514:1] 41616ci2 [0,0,0,-4745091,-3281245310] 4 [-2197107:-9741478:1331] 41616ci3 [0,0,0,9404349,-19108808894] 2 [26028596235807:-558454275055202:15568817473] 41616ci4 [0,0,0,-72163011,-235940487230] 4 [-510632252836794364915:-155686745042532784080:104591632943906893] 41616ci5 [0,0,0,-68417571,-261524089694] 2 [1468470115:262808972712:42875] 41616ci6 [0,0,0,-1154595171,-15100548367646] 2 [-339336939646496842432304840826381:78314799524323812380496226570:17297233011439963328709549917]
41616cj (4 curves)	1	2- 3- 17+	2- 3- -2 -2  0 -6 17+  0
Curve Equation t Generators 41616cj1 [0,0,0,-26571,1570426] 2 [69:256:1] 41616cj2 [0,0,0,-418251,104112250] 2 [293:2592:1] 41616cj3 [0,0,0,-3013131,-2013143366] 2 [-2203383:-45904:2197] 41616cj4 [0,0,0,-3037611,-1978768550] 2 [-867:1768:1]
41616ck (1 curve)	1	2- 3- 17+	2- 3- -2  3  4  1 17+ -7
Curve Equation t Generators 41616ck1 [0,0,0,204,799] 1 [9:58:1]
41616cl (4 curves)	1	2- 3- 17+	2- 3- -2  4  0 -2 17+  4
Curve Equation t Generators 41616cl1 [0,0,0,-28611,795906] 2 [-9:1026:1] 41616cl2 [0,0,0,-236691,-43774830] 4 [-7179:16226:27] 41616cl3 [0,0,0,-28611,-118059390] 2 [32932011:1958999750:9261] 41616cl4 [0,0,0,-3774051,-2822017374] 2 [-6872925327:127804222:6128487]
41616cm (2 curves)	1	2- 3- 17+	2- 3-  3 -2 -5 -1 17+  5
Curve Equation t Generators 41616cm1 [0,0,0,235824,-22717712] 1 [257:7407:1] 41616cm2 [0,0,0,-35137776,-80170805648] 1 [7708719212167571:-809918387650608003:551973381427]
41616cn (2 curves)	1	2- 3- 17+	2- 3-  3 -4  3 -1 17+  1
Curve Equation t Generators 41616cn1 [0,0,0,27744,-8568272] 1 [497:11313:1] 41616cn2 [0,0,0,-2469216,-1494259472] 1 [66028025:3938390919:15625]
41616co (2 curves)	1	2- 3- 17+	2- 3- -3  2  5 -1 17+  5
Curve Equation t Generators 41616co1 [0,0,0,816,-4624] 1 [17:119:1] 41616co2 [0,0,0,-121584,-16318096] 1 [3930587:69338563:6859]
41616cp (2 curves)	1	2- 3- 17+	2- 3- -3 -4 -3  2 17+ -8
Curve Equation t Generators 41616cp1 [0,0,0,-230979,-42962366] 1 [671:10206:1] 41616cp2 [0,0,0,-18737859,-31219652414] 1 [30047:5151006:1]
41616cq (1 curve)	1	2- 3- 17+	2- 3-  4  3  4 -5 17+ -1
Curve Equation t Generators 41616cq1 [0,0,0,-250563,411758530] 1 [5985:461840:1]
41616cr (2 curves)	1	2- 3- 17+	2- 3- -4 -2  0 -6 17+ -4
Curve Equation t Generators 41616cr1 [0,0,0,-104907,8302970] 2 [391:-5202:1] 41616cr2 [0,0,0,311253,57826010] 2 [119:-9826:1]
41616cs (2 curves)	0	2- 3- 17-	2- 3-  0  1  0 -1 17-  7
Curve Equation t 41616cs1 [0,0,0,810645,66315674] 1 41616cs2 [0,0,0,-9801435,-13319762038] 1
41616ct (1 curve)	0	2- 3- 17-	2- 3-  1 -4 -3  6 17- -4
Curve Equation t 41616ct1 [0,0,0,103173,-135471062] 1
41616cu (1 curve)	2	2- 3- 17-	2- 3-  2 -3 -4  1 17- -7
Curve Equation t Generators 41616cu1 [0,0,0,58956,3925487] 1 [121:3582:1]&[17629:2340900:1]
41616cv (1 curve)	0	2- 3- 17-	2- 3- -2 -1  0 -3 17- -1
Curve Equation t 41616cv1 [0,0,0,-648516,202037299] 1
41616cw (2 curves)	0	2- 3- 17-	2- 3-  3  4  3  2 17- -8
Curve Equation t 41616cw1 [0,0,0,-66752931,-211074104158] 1 41616cw2 [0,0,0,-5415241251,-153382152309982] 1
41616cx (1 curve)	2	2- 3- 17-	2- 3- -4 -3 -4 -5 17- -1
Curve Equation t Generators 41616cx1 [0,0,0,-867,83810] 1 [289:4896:1]&[17:-272:1]

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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