Cremona's table of elliptic curves

1258 = 2 · 17 · 37

Field	Data	Notes
Atkin-Lehner	2+ 17- 37+	Signs for the Atkin-Lehner involutions
Class	1258c	Isogeny class
Conductor	1258	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1100	Modular degree for the optimal curve
Δ	-21105737728 = -1 · 225 · 17 · 37	Discriminant
Eigenvalues	2+ -2 -2  1  2 -1 17- -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-637,-9384]	[a1,a2,a3,a4,a6]
j	-28520791922377/21105737728	j-invariant
L	0.46038383620352	L(r)(E,1)/r!
Ω	0.46038383620352	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10064e1 40256o1 11322q1 31450l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1258c1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-2	-2	1	2	-1	-	-8	-2	4	-2	+	-8	-6	8	12	10	12	9	-8	-6	10	15	-4	-7

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Quadratic twists for elliptic curve 1258c1

-4	8	-3	5	-7	17	37
10064e1	40256o1	11322q1	31450l1	61642f1	21386c1	46546d1

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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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