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	8	Product of Tamagawa factors cp
Δ	-138657927424 = -1 · 28 · 172 · 374	Discriminant
Eigenvalues	2+ -2  2  2  2  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,880,-14754]	[a1,a2,a3,a4,a6]
j	75488529485447/138657927424	j-invariant
L	1.0842607331364	L(r)(E,1)/r!
Ω	0.54213036656822	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	10064d2 40256r2 11322r2 31450n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1258b2

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 1258b2

-4	8	-3	5	-7	17	37
10064d2	40256r2	11322r2	31450n2	61642g2	21386d2	46546e2

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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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