Cremona's table of elliptic curves

15600 = 2⁴ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	15600bl	Isogeny class
Conductor	15600	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-2024755200 = -1 · 212 · 32 · 52 · 133	Discriminant
Eigenvalues	2- 3+ 5+  3  1 13- -5  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-728,8112]	[a1,a2,a3,a4,a6]
Generators	[26:78:1]	Generators of the group modulo torsion
j	-417267265/19773	j-invariant
L	4.8275630790194	L(r)(E,1)/r!
Ω	1.4573513440305	Real period
R	0.27604662725943	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	975h1 62400gp1 46800ef1 15600cp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15600bl1

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	1	-	-5	8	0	1	-3	-8	-2	-8	11	-11	-5	1	-3	-16	-4	-12	3	0	-2

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Quadratic twists for elliptic curve 15600bl1

-4	8	-3	5
975h1	62400gp1	46800ef1	15600cp1

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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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