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	12	Product of Tamagawa factors cp
Δ	-2215383048 = -1 · 23 · 34 · 434	Discriminant
Eigenvalues	2- 3+ -2  4  4  6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-304,-3175]	[a1,a2,a3,a4,a6]
j	-3107661785857/2215383048	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	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2064n4 8256w4 774b4 6450o4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258d4

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 258d4

-4	8	-3	5	-7	-11	13	17	-19	-43
2064n4	8256w4	774b4	6450o4	12642bi4	31218b3	43602b3	74562y3	93138q3	11094j4

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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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