Cremona's table of elliptic curves

2645 = 5 · 23²

Field	Data	Notes
Atkin-Lehner	5- 23-	Signs for the Atkin-Lehner involutions
Class	2645b	Isogeny class
Conductor	2645	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	-1520875 = -1 · 53 · 233	Discriminant
Eigenvalues	0 -2 5- -3 -6  4  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-15,-69]	[a1,a2,a3,a4,a6]
Generators	[15:57:1]	Generators of the group modulo torsion
j	-32768/125	j-invariant
L	1.7227109270906	L(r)(E,1)/r!
Ω	1.1032013324252	Real period
R	0.26025937370585	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	42320ba1 23805l1 13225a1 129605d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2645b1

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
0	-2	-	-3	-6	4	3	6	-	3	-5	3	9	-12	-6	3	-9	6	9	9	-2	-6	9	-6	-6

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Quadratic twists for elliptic curve 2645b1

-4	-3	5	-7	-23
42320ba1	23805l1	13225a1	129605d1	2645a1

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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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