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	258b	Isogeny class
Conductor	258	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1131994839168 = -1 · 27 · 314 · 432	Discriminant
Eigenvalues	2+ 3+ -2  2  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1276,53584]	[a1,a2,a3,a4,a6]
j	-230042158153417/1131994839168	j-invariant
L	0.7540903551457	L(r)(E,1)/r!
Ω	0.7540903551457	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	2064j2 8256m2 774h2 6450bf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258b2

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

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Quadratic twists for elliptic curve 258b2

-4	8	-3	5	-7	-11	13	17	-19	-43
2064j2	8256m2	774h2	6450bf2	12642s2	31218l2	43602r2	74562m2	93138bm2	11094s2

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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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