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	258a	Isogeny class
Conductor	258	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-8256 = -1 · 26 · 3 · 43	Discriminant
Eigenvalues	2+ 3+  1 -5  1 -3  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,3,-3]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	1685159/8256	j-invariant
L	1.0523025616395	L(r)(E,1)/r!
Ω	2.0851846863086	Real period
R	0.25232838331995	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2064l1 8256u1 774g1 6450bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258a1

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
+	+	1	-5	1	-3	0	-7	-4	-3	-2	2	8	+	7	-12	12	4	6	-8	0	-10	-3	-14	-7

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Quadratic twists for elliptic curve 258a1

-4	8	-3	5	-7	-11	13	17	-19	-43
2064l1	8256u1	774g1	6450bi1	12642n1	31218m1	43602n1	74562j1	93138bg1	11094r1

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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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