Cremona's table of elliptic curves

25840 = 2⁴ · 5 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 17+ 19-	Signs for the Atkin-Lehner involutions
Class	25840t	Isogeny class
Conductor	25840	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	212160	Modular degree for the optimal curve
Δ	-541904076800000 = -1 · 229 · 55 · 17 · 19	Discriminant
Eigenvalues	2- -3 5+ -4  3  4 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31003,2381002]	[a1,a2,a3,a4,a6]
Generators	[-131:2048:1]	Generators of the group modulo torsion
j	-804590545599729/132300800000	j-invariant
L	2.5283749284601	L(r)(E,1)/r!
Ω	0.50078152811932	Real period
R	1.2622145519002	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	3230c1 103360ci1 129200cn1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 25840t1

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	+	-4	3	4	+	-	5	2	-3	-9	5	5	-2	-6	0	2	2	7	-1	-1	-13	-12	12

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Quadratic twists for elliptic curve 25840t1

-4	8	5
3230c1	103360ci1	129200cn1

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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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