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	258d	Isogeny class
Conductor	258	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	1065024 = 26 · 32 · 432	Discriminant
Eigenvalues	2- 3+ -2  4  4  6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-344,-2599]	[a1,a2,a3,a4,a6]
j	4502751117697/1065024	j-invariant
L	1.6628412601244	L(r)(E,1)/r!
Ω	1.1085608400829	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2064n2 8256w2 774b2 6450o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258d2

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	4	4	6	-6	-4	-4	6	-8	2	2	+	4	-6	-12	10	12	-8	-6	-16	-12	10	2

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Quadratic twists for elliptic curve 258d2

-4	8	-3	5	-7	-11	13	17	-19	-43
2064n2	8256w2	774b2	6450o2	12642bi2	31218b2	43602b2	74562y2	93138q2	11094j2

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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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