Cremona's table of elliptic curves

2135 = 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	5+ 7+ 61+	Signs for the Atkin-Lehner involutions
Class	2135a	Isogeny class
Conductor	2135	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	-159537875 = -1 · 53 · 73 · 612	Discriminant
Eigenvalues	2  1 5+ 7+ -5  1  1 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-406,3075]	[a1,a2,a3,a4,a6]
Generators	[90:57:8]	Generators of the group modulo torsion
j	-7419438936064/159537875	j-invariant
L	5.7525885768481	L(r)(E,1)/r!
Ω	1.8192159699881	Real period
R	1.5810625763377	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34160t1 19215q1 10675g1 14945i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2135a1

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	1	+	+	-5	1	1	-4	0	-3	-6	2	2	10	13	0	0	+	2	-8	-14	-15	4	-4	7

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Quadratic twists for elliptic curve 2135a1

-4	-3	5	-7
34160t1	19215q1	10675g1	14945i1

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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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