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
deg	60	Modular degree for the optimal curve
Δ	528384 = 212 · 3 · 43	Discriminant
Eigenvalues	2- 3+ -2  4  4  6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-24,-39]	[a1,a2,a3,a4,a6]
j	1532808577/528384	j-invariant
L	1.6628412601244	L(r)(E,1)/r!
Ω	2.2171216801659	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	2064n1 8256w1 774b1 6450o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258d1

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 258d1

-4	8	-3	5	-7	-11	13	17	-19	-43
2064n1	8256w1	774b1	6450o1	12642bi1	31218b1	43602b1	74562y1	93138q1	11094j1

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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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