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	456d	Isogeny class
Conductor	456	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-15803136 = -1 · 28 · 32 · 193	Discriminant
Eigenvalues	2- 3+  1 -3 -5 -2 -1 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,55,93]	[a1,a2,a3,a4,a6]
Generators	[23:114:1]	Generators of the group modulo torsion
j	70575104/61731	j-invariant
L	1.6586130651212	L(r)(E,1)/r!
Ω	1.4353571813401	Real period
R	0.09629502483676	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	912c1 3648k1 1368c1 11400l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 456d1

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	-3	-5	-2	-1	-	4	-6	-10	0	0	-11	9	10	4	-5	-4	8	13	4	-4	-6	2

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Quadratic twists for elliptic curve 456d1

-4	8	-3	5	-7	-11	13	-19
912c1	3648k1	1368c1	11400l1	22344bd1	55176a1	77064b1	8664f1

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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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