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	258c	Isogeny class
Conductor	258	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-41796 = -1 · 22 · 35 · 43	Discriminant
Eigenvalues	2+ 3- -3 -3 -5 -3  0  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15,22]	[a1,a2,a3,a4,a6]
Generators	[5:-12:1]	Generators of the group modulo torsion
j	-338608873/41796	j-invariant
L	1.1803278628358	L(r)(E,1)/r!
Ω	3.5120735390641	Real period
R	0.033607720615964	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	2064h1 8256h1 774i1 6450y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258c1

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
+	-	-3	-3	-5	-3	0	7	-4	1	-6	-6	0	-	-3	12	-4	12	10	8	-16	-14	-9	2	1

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Quadratic twists for elliptic curve 258c1

-4	8	-3	5	-7	-11	13	17	-19	-43
2064h1	8256h1	774i1	6450y1	12642j1	31218q1	43602w1	74562f1	93138bd1	11094n1

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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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