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	258b	Isogeny class
Conductor	258	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	196	Modular degree for the optimal curve
Δ	1540767744 = 214 · 37 · 43	Discriminant
Eigenvalues	2+ 3+ -2  2  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1916,31440]	[a1,a2,a3,a4,a6]
j	778510269523657/1540767744	j-invariant
L	0.7540903551457	L(r)(E,1)/r!
Ω	1.5081807102914	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	2064j1 8256m1 774h1 6450bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 258b1

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	2	0	2	6	4	6	-2	4	4	-2	-	6	-4	-8	-12	4	0	-14	8	4	10	-2

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Quadratic twists for elliptic curve 258b1

-4	8	-3	5	-7	-11	13	17	-19	-43
2064j1	8256m1	774h1	6450bf1	12642s1	31218l1	43602r1	74562m1	93138bm1	11094s1

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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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