Cremona's table of elliptic curves

258 = 2 · 3 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 43-	Signs for the Atkin-Lehner involutions
Class	258g	Isogeny class
Conductor	258	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-33282 = -1 · 2 · 32 · 432	Discriminant
Eigenvalues	2- 3-  2 -2 -4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,8,2]	[a1,a2,a3,a4,a6]
j	56181887/33282	j-invariant
L	2.2471306373917	L(r)(E,1)/r!
Ω	2.2471306373917	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	2064f2 8256e2 774e2 6450b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258g2

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

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Quadratic twists for elliptic curve 258g2

-4	8	-3	5	-7	-11	13	17	-19	-43
2064f2	8256e2	774e2	6450b2	12642ba2	31218f2	43602l2	74562w2	93138f2	11094f2

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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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