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	2535f	Isogeny class
Conductor	2535	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	25413149385 = 34 · 5 · 137	Discriminant
Eigenvalues	1 3- 5+  0 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-18594,974287]	[a1,a2,a3,a4,a6]
j	147281603041/5265	j-invariant
L	2.2314748752379	L(r)(E,1)/r!
Ω	1.115737437619	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40560bg1 7605p1 12675e1 124215bd1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2535f1

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	8	-2	8	-6	6	-4	8	6	12	-2	4	0	6	16	4	-10	-18

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Quadratic twists for elliptic curve 2535f1

-4	-3	5	-7	13
40560bg1	7605p1	12675e1	124215bd1	195a1

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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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