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	2535g	Isogeny class
Conductor	2535	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	7488	Modular degree for the optimal curve
Δ	-550618236675 = -1 · 33 · 52 · 138	Discriminant
Eigenvalues	2 3- 5+  5  2 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-5126,144005]	[a1,a2,a3,a4,a6]
j	-18264064/675	j-invariant
L	5.5012852366595	L(r)(E,1)/r!
Ω	0.91688087277659	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40560bm1 7605t1 12675n1 124215bg1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2535g1

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	-	+	5	2	+	2	0	6	-4	-7	-2	6	1	-8	-4	12	-13	-7	12	15	3	8	14	-5

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Quadratic twists for elliptic curve 2535g1

-4	-3	5	-7	13
40560bm1	7605t1	12675n1	124215bg1	2535l1

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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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