Cremona's table of elliptic curves

105105 = 3 · 5 · 7² · 11 · 13

Class	r	Atkin-Lehner	Eigenvalues
105105a (1 curve)	0	3+ 5+ 7+ 11+ 13-	1 3+ 5+ 7+ 11+ 13- -1 -1
Curve Equation t 105105a1 [1,1,0,6982,420897] 1
105105b (1 curve)	2	3+ 5+ 7- 11+ 13+	0 3+ 5+ 7- 11+ 13+ -8 -8
Curve Equation t Generators 105105b1 [0,-1,1,-261,4892] 1 [-86:633:8]&[26:122:1]
105105c (2 curves)	0	3+ 5+ 7- 11+ 13+	1 3+ 5+ 7- 11+ 13+  2  2
Curve Equation t 105105c1 [1,1,0,-1539948,734684427] 2 105105c2 [1,1,0,-1325573,946787052] 2
105105d (4 curves)	0	3+ 5+ 7- 11+ 13+	1 3+ 5+ 7- 11+ 13+ -2  4
Curve Equation t 105105d1 [1,1,0,-3255928,2259953683] 2 105105d2 [1,1,0,-3275773,2230983952] 4 105105d3 [1,1,0,505802,7084257307] 2 105105d4 [1,1,0,-7374868,-4475955287] 2
105105e (2 curves)	0	3+ 5+ 7- 11+ 13+	1 3+ 5+ 7- 11+ 13+ -2 -8
Curve Equation t 105105e1 [1,1,0,-858,-11577] 2 105105e2 [1,1,0,-14333,-666462] 2
105105f (6 curves)	0	3+ 5+ 7- 11+ 13+	-1 3+ 5+ 7- 11+ 13+ -2  4
Curve Equation t 105105f1 [1,1,1,-441736,-134936152] 2 105105f2 [1,1,1,-7439181,-7812532806] 4 105105f3 [1,1,1,-7811826,-6987049602] 4 105105f4 [1,1,1,-119025656,-499864252966] 2 105105f5 [1,1,1,15129729,-40270657596] 2 105105f6 [1,1,1,-36715701,79134936348] 2
105105g (4 curves)	2	3+ 5+ 7- 11+ 13+	-1 3+ 5+ 7- 11+ 13+ -2 -4
Curve Equation t Generators 105105g1 [1,1,1,-2206,38954] 2 [28:-3:1]&[36:70:1] 105105g2 [1,1,1,-2451,29448] 4 [-39:279:1]&[-36:287:1] 105105g3 [1,1,1,7104,212904] 2 [-18:3555:8]&[3:482:1] 105105g4 [1,1,1,-15926,-757492] 2 [-71:182:1]&[-63:58:1]
105105h (6 curves)	0	3+ 5+ 7- 11+ 13+	-1 3+ 5+ 7- 11+ 13+ -2 -4
Curve Equation t 105105h1 [1,1,1,-2963014076,-62079833134852] 2 105105h2 [1,1,1,-3058717201,-57855535478602] 4 105105h3 [1,1,1,4451910924,-297366462133602] 2 105105h4 [1,1,1,-12100595326,452012355238898] 4 105105h5 [1,1,1,18335185049,2359739243456048] 2 105105h6 [1,1,1,-187206425701,31176011310504248] 2
105105i (4 curves)	0	3+ 5+ 7- 11+ 13+	-1 3+ 5+ 7- 11+ 13+  6  0
Curve Equation t 105105i1 [1,1,1,-21561,-45631986] 2 105105i2 [1,1,1,-2050406,-1118485222] 4 105105i3 [1,1,1,-3856301,1147551824] 2 105105i4 [1,1,1,-32706031,-72006552472] 2
105105j (1 curve)	0	3+ 5+ 7- 11+ 13+	2 3+ 5+ 7- 11+ 13+ -5  5
Curve Equation t 105105j1 [0,-1,1,-19167346,-32521820829] 1
105105k (1 curve)	0	3+ 5+ 7- 11+ 13+	-2 3+ 5+ 7- 11+ 13+ -7  5
Curve Equation t 105105k1 [0,-1,1,-138336,142874696] 1
105105l (2 curves)	1	3+ 5+ 7- 11+ 13-	1 3+ 5+ 7- 11+ 13- -8 -4
Curve Equation t Generators 105105l1 [1,1,0,-38153483,126368226048] 2 [9472:779424:1] 105105l2 [1,1,0,-674920978,6747603992557] 2 [14308:135001:1]
105105m (2 curves)	1	3+ 5+ 7- 11+ 13-	-1 3+ 5+ 7- 11+ 13-  2  2
Curve Equation t Generators 105105m1 [1,1,1,-981,35034] 2 [6:-175:1] 105105m2 [1,1,1,-23276,1354898] 2 [104:-322:1]
105105n (1 curve)	1	3+ 5+ 7- 11+ 13-	2 3+ 5+ 7- 11+ 13-  5 -1
Curve Equation t Generators 105105n1 [0,-1,1,-1821346,-987983823] 1 [31877648:2766436081:4096]
105105o (2 curves)	1	3+ 5+ 7- 11- 13+	-1 3+ 5+ 7- 11- 13+  0  0
Curve Equation t Generators 105105o1 [1,1,1,-176,18248] 2 [-4:139:1] 105105o2 [1,1,1,-11551,468698] 2 [-34:924:1]
105105p (1 curve)	1	3+ 5+ 7- 11- 13+	2 3+ 5+ 7- 11- 13+  0  2
Curve Equation t Generators 105105p1 [0,-1,1,-70086,8946167] 1 [-2422:12191:8]
105105q (1 curve)	1	3+ 5+ 7- 11- 13+	2 3+ 5+ 7- 11- 13+  3 -1
Curve Equation t Generators 105105q1 [0,-1,1,-26068491626,1620036763297091] 1 [22518610:32317625841:1000]
105105r (1 curve)	0	3+ 5+ 7- 11- 13-	0 3+ 5+ 7- 11- 13- -5 -6
Curve Equation t 105105r1 [0,-1,1,-108901,14079666] 1
105105s (2 curves)	0	3+ 5+ 7- 11- 13-	1 3+ 5+ 7- 11- 13-  6 -2
Curve Equation t 105105s1 [1,1,0,3062,77407] 2 105105s2 [1,1,0,-19233,741798] 2
105105t (4 curves)	0	3+ 5+ 7- 11- 13-	1 3+ 5+ 7- 11- 13-  6  4
Curve Equation t 105105t1 [1,1,0,-3553,441232] 2 105105t2 [1,1,0,-111598,14249383] 4 105105t3 [1,1,0,-168193,-1812278] 2 105105t4 [1,1,0,-1783723,916193608] 2
105105u (4 curves)	0	3+ 5+ 7- 11- 13-	-1 3+ 5+ 7- 11- 13-  2  4
Curve Equation t 105105u1 [1,1,1,-64681,6285278] 4 105105u2 [1,1,1,-94326,-94326] 4 105105u3 [1,1,1,377299,-282976] 2 105105u4 [1,1,1,-1040271,-407607432] 2
105105v (1 curve)	0	3+ 5- 7+ 11- 13-	2 3+ 5- 7+ 11- 13- -7 -2
Curve Equation t 105105v1 [0,-1,1,98670,-1103047] 1
105105w (2 curves)	1	3+ 5- 7- 11+ 13+	0 3+ 5- 7- 11+ 13+  3 -2
Curve Equation t Generators 105105w1 [0,-1,1,285,713] 1 [23:137:1] 105105w2 [0,-1,1,-5175,148406] 1 [230:3327:1]
105105x (2 curves)	1	3+ 5- 7- 11+ 13+	1 3+ 5- 7- 11+ 13+ -4  2
Curve Equation t Generators 105105x1 [1,1,0,-575432,-88383861] 2 [-342:8451:1] 105105x2 [1,1,0,-4343287,3420996286] 2 [-938:82144:1]
105105y (1 curve)	1	3+ 5- 7- 11+ 13+	2 3+ 5- 7- 11+ 13+  3  0
Curve Equation t Generators 105105y1 [0,-1,1,2280,390431] 1 [730:9291:8]
105105z (1 curve)	1	3+ 5- 7- 11+ 13+	-2 3+ 5- 7- 11+ 13+  1  2
Curve Equation t Generators 105105z1 [0,-1,1,23210,14959986] 1 [-770:481094:125]
105105ba (1 curve)	1	3+ 5- 7- 11+ 13+	-2 3+ 5- 7- 11+ 13+  8  2
Curve Equation t Generators 105105ba1 [0,-1,1,16576390,-62298095602] 1 [78139:21870537:1]
105105bb (1 curve)	0	3+ 5- 7- 11+ 13-	0 3+ 5- 7- 11+ 13- -3  1
Curve Equation t 105105bb1 [0,-1,1,-981045,-373684984] 1
105105bc (1 curve)	0	3+ 5- 7- 11+ 13-	0 3+ 5- 7- 11+ 13-  4  8
Curve Equation t 105105bc1 [0,-1,1,-3502366205,79780509547703] 1
105105bd (2 curves)	0	3+ 5- 7- 11+ 13-	1 3+ 5- 7- 11+ 13- -2 -2
Curve Equation t 105105bd1 [1,1,0,-1112227,451016224] 2 105105bd2 [1,1,0,-1103652,458323839] 2
105105be (4 curves)	2	3+ 5- 7- 11+ 13-	-1 3+ 5- 7- 11+ 13- -2 -4
Curve Equation t Generators 105105be1 [1,1,1,3135,-199578] 4 [90:861:1]&[297:5051:1] 105105be2 [1,1,1,-38270,-2617630] 4 [-1106:2419:8]&[-120:574:1] 105105be3 [1,1,1,-143375,18024992] 2 [-428:1316:1]&[-148:6076:1] 105105be4 [1,1,1,-595645,-177187480] 2 [-445:249:1]&[10534:285789:8]
105105bf (2 curves)	0	3+ 5- 7- 11- 13+	0 3+ 5- 7- 11- 13+  0  4
Curve Equation t 105105bf1 [0,-1,1,-3590785,-2726230452] 1 105105bf2 [0,-1,1,18675305,-6599351319] 1
105105bg (2 curves)	0	3+ 5- 7- 11- 13+	0 3+ 5- 7- 11- 13+  3  7
Curve Equation t 105105bg1 [0,-1,1,-23585,-1661059] 1 105105bg2 [0,-1,1,170455,11664638] 1
105105bh (2 curves)	0	3+ 5- 7- 11- 13+	1 3+ 5- 7- 11- 13+ -2  2
Curve Equation t 105105bh1 [1,1,0,-136651372,-1243662803669] 2 105105bh2 [1,1,0,-2759635827,-55763443894626] 2
105105bi (2 curves)	2	3+ 5- 7- 11- 13+	-1 3+ 5- 7- 11- 13+ -4 -4
Curve Equation t Generators 105105bi1 [1,1,1,90,90] 2 [0:9:1]&[3:18:1] 105105bi2 [1,1,1,-365,272] 2 [-18:46:1]&[-13:61:1]
105105bj (1 curve)	0	3+ 5- 7- 11- 13+	-2 3+ 5- 7- 11- 13+  7 -1
Curve Equation t 105105bj1 [0,-1,1,-543720,4705621598] 1
105105bk (4 curves)	1	3+ 5- 7- 11- 13-	1 3+ 5- 7- 11- 13-  2  4
Curve Equation t Generators 105105bk1 [1,1,0,10168063,-16409280096] 2 [1880796:-497851358:27] 105105bk2 [1,1,0,-68596742,-166897316529] 4 [80086:3055777:8] 105105bk3 [1,1,0,-373792997,2641701739734] 4 [-169826:8128663:8] 105105bk4 [1,1,0,-1023637367,-12605155408404] 2 [2236086:-1175198223:8]
105105bl (1 curve)	1	3+ 5- 7- 11- 13-	2 3+ 5- 7- 11- 13-  7 -7
Curve Equation t Generators 105105bl1 [0,-1,1,110,-99] 1 [68:241:64]
105105bm (1 curve)	1	3+ 5- 7- 11- 13-	-2 3+ 5- 7- 11- 13-  4 -2
Curve Equation t Generators 105105bm1 [0,-1,1,40360,-295282] 1 [82:1886:1]
105105bn (2 curves)	1	3- 5+ 7+ 11+ 13-	0 3- 5+ 7+ 11+ 13- -3  2
Curve Equation t Generators 105105bn1 [0,1,1,13949,-272555] 3 [325:6220:1] 105105bn2 [0,1,1,-253591,-50396174] 1 [4678580:10301933:8000]
105105bo (1 curve)	1	3- 5+ 7+ 11+ 13-	2 3- 5+ 7+ 11+ 13- -3  0
Curve Equation t Generators 105105bo1 [0,1,1,111704,-134141339] 1 [8458:273269:8]
105105bp (1 curve)	1	3- 5+ 7+ 11+ 13-	-2 3- 5+ 7+ 11+ 13- -1 -2
Curve Equation t Generators 105105bp1 [0,1,1,474,-43480] 1 [1020:4645:27]
105105bq (2 curves)	1	3- 5+ 7- 11+ 13+	1 3- 5+ 7- 11+ 13+  2  2
Curve Equation t Generators 105105bq1 [1,0,1,-22699,-1318159] 2 [2131817:40205911:4913] 105105bq2 [1,0,1,-22524,-1339439] 2 [1691:68412:1]
105105br (6 curves)	1	3- 5+ 7- 11+ 13+	-1 3- 5+ 7- 11+ 13+ -2 -4
Curve Equation t Generators 105105br1 [1,0,0,859949,-440888344] 2 [1793:81965:1] 105105br2 [1,0,0,-6137496,-4595971185] 4 [-1317:35346:1] 105105br3 [1,0,0,-32015621,65756299440] 4 [-3467:369271:1] 105105br4 [1,0,0,-92218491,-340845553854] 2 [11190:163014:1] 105105br5 [1,0,0,26031004,277707745965] 2 [-1556:483931:1] 105105br6 [1,0,0,-504112246,4356453685415] 2 [-13807:2953886:1]
105105bs (6 curves)	1	3- 5+ 7- 11+ 13+	-1 3- 5+ 7- 11+ 13+  6 -4
Curve Equation t Generators 105105bs1 [1,0,0,29644,-539505] 2 [53553:2367290:27] 105105bs2 [1,0,0,-123481,-4428880] 4 [-307:2291:1] 105105bs3 [1,0,0,-1158606,476490195] 4 [-1137:18576:1] 105105bs4 [1,0,0,-1538356,-733655455] 2 [-19608:31673:27] 105105bs5 [1,0,0,-378281,1108085250] 2 [-1046:19486:1] 105105bs6 [1,0,0,-18500931,30627856440] 2 [2484:-1194:1]
105105bt (2 curves)	0	3- 5+ 7- 11+ 13-	1 3- 5+ 7- 11+ 13-  4 -2
Curve Equation t 105105bt1 [1,0,1,-11744,256001] 2 105105bt2 [1,0,1,-88639,-9986413] 2
105105bu (1 curve)	2	3- 5+ 7- 11+ 13-	-2 3- 5+ 7- 11+ 13- -8 -2
Curve Equation t Generators 105105bu1 [0,1,1,338294,181723756] 1 [-376:1228:1]&[137:-15188:1]
105105bv (2 curves)	0	3- 5+ 7- 11- 13+	1 3- 5+ 7- 11- 13+  6  0
Curve Equation t 105105bv1 [1,0,1,2326,-26953] 2 105105bv2 [1,0,1,-11149,-237163] 2
105105bw (4 curves)	0	3- 5+ 7- 11- 13+	1 3- 5+ 7- 11- 13+ -6  0
Curve Equation t 105105bw1 [1,0,1,-3558259,2583179057] 2 105105bw2 [1,0,1,-3558504,2582805481] 4 105105bw3 [1,0,1,-3103049,3268356347] 2 105105bw4 [1,0,1,-4017879,1873346731] 2
105105bx (8 curves)	0	3- 5+ 7- 11- 13+	-1 3- 5+ 7- 11- 13+ -2 -4
Curve Equation t 105105bx1 [1,0,0,-218585571,-1243903555224] 2 105105bx2 [1,0,0,-218585816,-1243900627425] 4 105105bx3 [1,0,0,-215002691,-1286649458550] 2 105105bx4 [1,0,0,-222172861,-1200964416184] 4 105105bx5 [1,0,0,183637544,-5096013845455] 2 105105bx6 [1,0,0,-685375986,5442016880691] 4 105105bx7 [1,0,0,1524860889,33310009542816] 2 105105bx8 [1,0,0,-10306862861,402726680031066] 2
105105by (6 curves)	0	3- 5+ 7- 11- 13+	-1 3- 5+ 7- 11- 13+ -2 -4
Curve Equation t 105105by1 [1,0,0,-190366,-61749325] 2 105105by2 [1,0,0,-3777411,-2824491384] 4 105105by3 [1,0,0,-4518536,-1637653809] 4 105105by4 [1,0,0,-60429006,-180812472555] 2 105105by5 [1,0,0,15976939,-12364985424] 2 105105by6 [1,0,0,-36872011,85050247106] 2
105105bz (1 curve)	0	3- 5+ 7- 11- 13+	2 3- 5+ 7- 11- 13+  7  2
Curve Equation t 105105bz1 [0,1,1,2014,3791] 1
105105ca (1 curve)	0	3- 5+ 7- 11- 13+	2 3- 5+ 7- 11- 13+ -7  7
Curve Equation t 105105ca1 [0,1,1,5374,23111] 1
105105cb (1 curve)	2	3- 5+ 7- 11- 13+	-2 3- 5+ 7- 11- 13+ -4  2
Curve Equation t Generators 105105cb1 [0,1,1,824,1096] 1 [32:247:1]&[2:52:1]
105105cc (4 curves)	1	3- 5+ 7- 11- 13-	1 3- 5+ 7- 11- 13- -6 -4
Curve Equation t Generators 105105cc1 [1,0,1,-57454,9112331] 2 [38574:2656109:8] 105105cc2 [1,0,1,-1092579,439310281] 4 [-667:29853:1] 105105cc3 [1,0,1,-1267754,288940061] 2 [-2844144:-116908313:4096] 105105cc4 [1,0,1,-17479404,28126489801] 2 [681437633936:-344400487313:282300416]
105105cd (2 curves)	1	3- 5+ 7- 11- 13-	-1 3- 5+ 7- 11- 13-  4  4
Curve Equation t Generators 105105cd1 [1,0,0,4409,-17704] 2 [229:3493:1] 105105cd2 [1,0,0,-17886,-147015] 2 [-27:576:1]
105105ce (1 curve)	1	3- 5+ 7- 11- 13-	-2 3- 5+ 7- 11- 13- -3 -1
Curve Equation t Generators 105105ce1 [0,1,1,474,326] 1 [9:-74:1]
105105cf (1 curve)	0	3- 5- 7+ 11- 13+	0 3- 5- 7+ 11- 13+  5  6
Curve Equation t 105105cf1 [0,1,1,-5336165,-4818653206] 1
105105cg (1 curve)	0	3- 5- 7- 11+ 13+	1 3- 5- 7- 11+ 13+  1  1
Curve Equation t 105105cg1 [1,0,1,142,-1207] 1
105105ch (4 curves)	0	3- 5- 7- 11+ 13+	1 3- 5- 7- 11+ 13+  6 -8
Curve Equation t 105105ch1 [1,0,1,108607,14007431] 2 105105ch2 [1,0,1,-632518,133180331] 4 105105ch3 [1,0,1,-3906943,-2870122279] 2 105105ch4 [1,0,1,-9216093,10766513041] 2
105105ci (2 curves)	0	3- 5- 7- 11+ 13+	1 3- 5- 7- 11+ 13+  8  4
Curve Equation t 105105ci1 [1,0,1,-778643,-368531719] 2 105105ci2 [1,0,1,-13773898,-19674282547] 2
105105cj (1 curve)	1	3- 5- 7- 11+ 13-	0 3- 5- 7- 11+ 13- -7  5
Curve Equation t Generators 105105cj1 [0,1,1,-328855,72707506] 1 [590:9187:1]
105105ck (2 curves)	1	3- 5- 7- 11+ 13-	1 3- 5- 7- 11+ 13- -2 -2
Curve Equation t Generators 105105ck1 [1,0,1,-31428,-2146427] 2 [299:3750:1] 105105ck2 [1,0,1,-27053,-2764177] 2 [309:4135:1]
105105cl (4 curves)	1	3- 5- 7- 11+ 13-	-1 3- 5- 7- 11+ 13-  2 -8
Curve Equation t Generators 105105cl1 [1,0,0,-9605,359400] 4 [61:7:1] 105105cl2 [1,0,0,-15730,-156325] 4 [-115:425:1] 105105cl3 [1,0,0,61445,-1221340] 2 [32:866:1] 105105cl4 [1,0,0,-190905,-32073210] 2 [-258:282:1]
105105cm (1 curve)	1	3- 5- 7- 11+ 13-	-2 3- 5- 7- 11+ 13-  7 -5
Curve Equation t Generators 105105cm1 [0,1,1,-6778480,-48992463866] 1 [9326:-836063:1]
105105cn (1 curve)	1	3- 5- 7- 11- 13+	2 3- 5- 7- 11- 13+  7 -1
Curve Equation t Generators 105105cn1 [0,1,1,-97820,-11809801] 1 [4538:85991:8]
105105co (1 curve)	0	3- 5- 7- 11- 13-	0 3- 5- 7- 11- 13-  4 -4
Curve Equation t 105105co1 [0,1,1,-65299915,-207723218069] 1
105105cp (2 curves)	0	3- 5- 7- 11- 13-	-1 3- 5- 7- 11- 13-  0  0
Curve Equation t 105105cp1 [1,0,0,-8625,-6285000] 2 105105cp2 [1,0,0,-566000,-162461475] 2
105105cq (1 curve)	0	3- 5- 7- 11- 13-	2 3- 5- 7- 11- 13-  0 -2
Curve Equation t 105105cq1 [0,1,1,-1430,-26491] 1
105105cr (1 curve)	0	3- 5- 7- 11- 13-	2 3- 5- 7- 11- 13- -3  1
Curve Equation t 105105cr1 [0,1,1,-1277356089690,-555670055098722931] 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