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	3	Product of Tamagawa factors cp
Δ	1032 = 23 · 3 · 43	Discriminant
Eigenvalues	2- 3+ -2  4  4  6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5504,-159463]	[a1,a2,a3,a4,a6]
j	18440127492397057/1032	j-invariant
L	1.6628412601244	L(r)(E,1)/r!
Ω	0.55428042004147	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2064n3 8256w3 774b3 6450o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258d3

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 258d3

-4	8	-3	5	-7	-11	13	17	-19	-43
2064n3	8256w3	774b3	6450o3	12642bi3	31218b4	43602b4	74562y4	93138q4	11094j3

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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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