Cremona's table of elliptic curves

2600 = 2³ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	2600a	Isogeny class
Conductor	2600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	260000000 = 28 · 57 · 13	Discriminant
Eigenvalues	2+ -2 5+  0  2 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-508,-4512]	[a1,a2,a3,a4,a6]
Generators	[-13:8:1]	Generators of the group modulo torsion
j	3631696/65	j-invariant
L	2.3307822970095	L(r)(E,1)/r!
Ω	1.006547240562	Real period
R	2.31562136687	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5200b1 20800ba1 23400bg1 520b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2600a1

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	+	0	2	+	-2	2	-2	-6	2	6	2	-6	8	2	6	-14	0	10	2	-4	-12	-6	-2

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Quadratic twists for elliptic curve 2600a1

-4	8	-3	5	-7	13
5200b1	20800ba1	23400bg1	520b1	127400l1	33800u1

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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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