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	4	Product of Tamagawa factors cp
Δ	-1038891501716445 = -1 · 316 · 5 · 136	Discriminant
Eigenvalues	1 3+ 5+  0  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-18593,-1840002]	[a1,a2,a3,a4,a6]
Generators	[1030259354038:-34012477141865:958585256]	Generators of the group modulo torsion
j	-147281603041/215233605	j-invariant
L	3.1956681160408	L(r)(E,1)/r!
Ω	0.19422869560389	Real period
R	16.453120410993	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	40560ca7 7605q8 12675x8 124215cv7	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2535a8

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 2535a8

-4	-3	5	-7	13
40560ca7	7605q8	12675x8	124215cv7	15a6

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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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