Cremona's table of elliptic curves

25584 = 2⁴ · 3 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 41+	Signs for the Atkin-Lehner involutions
Class	25584l	Isogeny class
Conductor	25584	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	259200	Modular degree for the optimal curve
Δ	31403120787792 = 24 · 312 · 133 · 412	Discriminant
Eigenvalues	2- 3+ -2 -2  2 13+ -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1230809,-525164160]	[a1,a2,a3,a4,a6]
j	12887719410278499008512/1962695049237	j-invariant
L	0.14333487216194	L(r)(E,1)/r!
Ω	0.14333487216198	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	6396c1 102336cl1 76752bw1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 25584l1

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	2	+	-2	-6	8	-6	-10	2	+	-12	2	-10	-2	-2	2	-2	-14	8	18	-2	-6

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Quadratic twists for elliptic curve 25584l1

-4	8	-3
6396c1	102336cl1	76752bw1

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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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