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	1258b	Isogeny class
Conductor	1258	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	704	Modular degree for the optimal curve
Δ	1525219328 = 216 · 17 · 372	Discriminant
Eigenvalues	2+ -2  2  2  2  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-400,-2466]	[a1,a2,a3,a4,a6]
j	7052482298233/1525219328	j-invariant
L	1.0842607331364	L(r)(E,1)/r!
Ω	1.0842607331364	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10064d1 40256r1 11322r1 31450n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1258b1

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	2	2	2	-	4	6	-6	-6	+	10	-4	-8	-2	12	-6	4	6	10	6	0	14	10

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Quadratic twists for elliptic curve 1258b1

-4	8	-3	5	-7	17	37
10064d1	40256r1	11322r1	31450n1	61642g1	21386d1	46546e1

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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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