Cremona's table of elliptic curves

109174 = 2 · 13² · 17 · 19

Class	r	Atkin-Lehner	Eigenvalues
109174a (2 curves)	1	2+ 13+ 17+ 19+	2+  0  2  2  2 13+ 17+ 19+
Curve Equation t Generators 109174a1 [1,-1,0,-68561,6906589] 2 [2030:18251:8] 109174a2 [1,-1,0,-1096081,441958557] 2 [39316:6607:64]
109174b (4 curves)	1	2+ 13+ 17+ 19+	2+ -2  0 -2  6 13+ 17+ 19+
Curve Equation t Generators 109174b1 [1,0,1,85679,21429540] 2 [1876:81435:1] 109174b2 [1,0,1,-833681,254211492] 2 [755:7058:1] 109174b3 [1,0,1,-793121,-677321916] 2 [2266146548193:159184093338470:437245479] 109174b4 [1,0,1,-17399061,-27904421140] 2 [560847:78777256:27]
109174c (2 curves)	1	2+ 13+ 17+ 19+	2+ -2  2  2  0 13+ 17+ 19+
Curve Equation t Generators 109174c1 [1,0,1,-7801720,8386869714] 2 [160220:2695737:125] 109174c2 [1,0,1,-7823690,8337252666] 2 [1980:23702:1]
109174d (2 curves)	0	2+ 13+ 17+ 19-	2+  2 -2  0  4 13+ 17+ 19-
Curve Equation t 109174d1 [1,1,0,-13016,-103696] 2 109174d2 [1,1,0,51204,-758740] 2
109174e (2 curves)	2	2+ 13+ 17+ 19-	2+ -2 -4 -4 -2 13+ 17+ 19-
Curve Equation t Generators 109174e1 [1,0,1,-40733,3145092] 2 [261:3080:1]&[-81:2472:1] 109174e2 [1,0,1,-650823,202034432] 2 [470:-397:1]&[3862:3199:8]
109174f (4 curves)	2	2+ 13+ 17- 19+	2+ -2  0 -2  0 13+ 17- 19+
Curve Equation t Generators 109174f1 [1,0,1,-25861,1135344] 2 [-116:1663:1]&[-38:1455:1] 109174f2 [1,0,1,-154301,-22446240] 2 [-224:1055:1]&[-220:1039:1] 109174f3 [1,0,1,-772841,-261502824] 2 [-506:506:1]&[1249:26246:1] 109174f4 [1,0,1,-12364551,-16735641076] 2 [4434:122758:1]&[18204:2397307:1]
109174g (1 curve)	1	2+ 13+ 17- 19-	2+ -2 -1 -2  3 13+ 17- 19-
Curve Equation t Generators 109174g1 [1,0,1,20276,120330] 1 [440:9489:1]
109174h (2 curves)	1	2+ 13- 17+ 19-	2+  0  0  4  2 13- 17+ 19-
Curve Equation t Generators 109174h1 [1,-1,0,-37712,2829568] 2 [201:1727:1] 109174h2 [1,-1,0,-603472,180591360] 2 [58405:56131:125]
109174i (2 curves)	2	2- 13+ 17+ 19+	2-  0 -4  2 -4 13+ 17+ 19+
Curve Equation t Generators 109174i1 [1,-1,1,-21157,-1177315] 2 [-85:80:1]&[-674:671:8] 109174i2 [1,-1,1,-14397,-1947955] 2 [253:3122:1]&[2654:42271:8]
109174j (2 curves)	1	2- 13+ 17+ 19-	2- -2  0  2  6 13+ 17+ 19-
Curve Equation t Generators 109174j1 [1,0,0,-14453,805921] 2 [92:461:1] 109174j2 [1,0,0,-244293,46452145] 2 [-272:9769:1]
109174k (2 curves)	1	2- 13+ 17+ 19-	2- -2  2  2  0 13+ 17+ 19-
Curve Equation t Generators 109174k1 [1,0,0,-45042,1289092] 2 [-142:2268:1] 109174k2 [1,0,0,-396562,-95238300] 2 [-350:1020:1]
109174l (2 curves)	1	2- 13+ 17- 19+	2-  2  0  2  4 13+ 17- 19+
Curve Equation t Generators 109174l1 [1,1,1,-2202158,1237437547] 2 [2735:123861:1] 109174l2 [1,1,1,-35082798,79966841963] 2 [3459:2299:1]
109174m (4 curves)	1	2- 13+ 17- 19+	2- -2  0 -2  0 13+ 17- 19+
Curve Equation t Generators 109174m1 [1,0,0,-3696118,-2395045056] 2 [-58124:962787:64] 109174m2 [1,0,0,-15287828,20582042506] 2 [107654:11950723:8] 109174m3 [1,0,0,-288913193,-1890186709607] 2 [-17472444448692:8757376643021:1780360128] 109174m4 [1,0,0,-289041633,-1888422021071] 2 [128920309852011888300:-277597794531222537261259:27818127000000]
109174n (1 curve)	1	2- 13+ 17- 19+	2- -2  1  2 -3 13+ 17- 19+
Curve Equation t Generators 109174n1 [1,0,0,120,64] 1 [0:8:1]
109174o (2 curves)	0	2- 13+ 17- 19-	2-  0  0  0  2 13+ 17- 19-
Curve Equation t 109174o1 [1,-1,1,-7975,171643] 2 109174o2 [1,-1,1,24135,1186319] 2
109174p (2 curves)	0	2- 13+ 17- 19-	2-  2  0 -4  4 13+ 17- 19-
Curve Equation t 109174p1 [1,1,1,-18678,875363] 2 109174p2 [1,1,1,25262,4425715] 2
109174q (2 curves)	0	2- 13+ 17- 19-	2-  2  2 -2 -6 13+ 17- 19-
Curve Equation t 109174q1 [1,1,1,-2841992,-1840023047] 2 109174q2 [1,1,1,-1621812,-3429185479] 2
109174r (2 curves)	1	2- 13- 17+ 19+	2-  0  0 -4 -2 13- 17+ 19+
Curve Equation t Generators 109174r1 [1,-1,1,-6373360,6197440851] 2 [1437:-2895:1] 109174r2 [1,-1,1,-101986800,396453257555] 2 [-4605:878905:1]

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

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