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	2600j	Isogeny class
Conductor	2600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	260000000 = 28 · 57 · 13	Discriminant
Eigenvalues	2-  0 5+  0 -4 13-  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-575,5250]	[a1,a2,a3,a4,a6]
Generators	[-10:100:1]	Generators of the group modulo torsion
j	5256144/65	j-invariant
L	3.113756279085	L(r)(E,1)/r!
Ω	1.7533532688495	Real period
R	1.7758864311059	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5200e1 20800a1 23400o1 520a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2600j1

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	+	0	-4	-	6	4	0	-2	-4	6	-6	-8	0	-2	4	-10	-12	-4	-14	-16	-12	2	2

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Quadratic twists for elliptic curve 2600j1

-4	8	-3	5	-7	13
5200e1	20800a1	23400o1	520a1	127400bh1	33800a1

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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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