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	2135b	Isogeny class
Conductor	2135	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	73576	Modular degree for the optimal curve
Δ	-4328090712731986235 = -1 · 5 · 717 · 612	Discriminant
Eigenvalues	-2  1 5+ 7+ -5  1 -7  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1123066,468529056]	[a1,a2,a3,a4,a6]
j	-156653440431604480405504/4328090712731986235	j-invariant
L	0.49014783653557	L(r)(E,1)/r!
Ω	0.24507391826778	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	34160u1 19215t1 10675k1 14945g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2135b1

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	-7	8	-4	-3	-2	10	6	-6	5	8	0	-	6	0	-6	1	12	-4	-1

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Quadratic twists for elliptic curve 2135b1

-4	-3	5	-7
34160u1	19215t1	10675k1	14945g1

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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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