Cremona's table of elliptic curves

456 = 2³ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 19-	Signs for the Atkin-Lehner involutions
Class	456c	Isogeny class
Conductor	456	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-3545856 = -1 · 28 · 36 · 19	Discriminant
Eigenvalues	2+ 3- -3 -3 -1 -2 -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-57,171]	[a1,a2,a3,a4,a6]
Generators	[3:6:1]	Generators of the group modulo torsion
j	-81415168/13851	j-invariant
L	1.8547501445298	L(r)(E,1)/r!
Ω	2.4058503308937	Real period
R	0.032122221000076	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	912a1 3648d1 1368i1 11400ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 456c1

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	-1	-2	-5	-	-4	-6	-2	8	-8	13	13	-6	4	-13	4	-8	-3	-4	4	-6	2

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Quadratic twists for elliptic curve 456c1

-4	8	-3	5	-7	-11	13	-19
912a1	3648d1	1368i1	11400ba1	22344e1	55176n1	77064u1	8664k1

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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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