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	2135g	Isogeny class
Conductor	2135	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	-1780556640625 = -1 · 510 · 72 · 612	Discriminant
Eigenvalues	-1 -2 5- 7+  2 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3710,107797]	[a1,a2,a3,a4,a6]
Generators	[-41:458:1]	Generators of the group modulo torsion
j	-5647454716105441/1780556640625	j-invariant
L	1.400081320843	L(r)(E,1)/r!
Ω	0.79143671543098	Real period
R	0.17690376167103	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	34160bg2 19215h2 10675i2 14945d2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2135g2

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	-2	-	+	2	-2	-2	-4	4	-6	-2	10	6	12	-2	-2	-6	-	0	-6	6	10	-6	-2	-10

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Quadratic twists for elliptic curve 2135g2

-4	-3	5	-7
34160bg2	19215h2	10675i2	14945d2

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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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