Cremona's table of elliptic curves

2535 = 3 · 5 · 13²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	2535a	Isogeny class
Conductor	2535	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	244357205625 = 34 · 54 · 136	Discriminant
Eigenvalues	1 3+ 5+  0  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1693,-13112]	[a1,a2,a3,a4,a6]
Generators	[-226:1031:8]	Generators of the group modulo torsion
j	111284641/50625	j-invariant
L	3.1956681160408	L(r)(E,1)/r!
Ω	0.77691478241555	Real period
R	4.1132801027481	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	40560ca3 7605q4 12675x3 124215cv3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2535a3

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
1	+	+	0	4	+	2	-4	0	-2	0	10	-10	4	-8	-10	4	-2	-12	8	-10	0	-12	6	-2

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Quadratic twists for elliptic curve 2535a3

-4	-3	5	-7	13
40560ca3	7605q4	12675x3	124215cv3	15a1

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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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