Cremona's table of elliptic curves

2117 = 29 · 73

Field	Data	Notes
Atkin-Lehner	29- 73+	Signs for the Atkin-Lehner involutions
Class	2117a	Isogeny class
Conductor	2117	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	152	Modular degree for the optimal curve
Δ	2117 = 29 · 73	Discriminant
Eigenvalues	-2 -2  0 -2 -3 -4 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-8,6]	[a1,a2,a3,a4,a6]
Generators	[0:2:1] [1:0:1]	Generators of the group modulo torsion
j	64000000/2117	j-invariant
L	1.5083304029051	L(r)(E,1)/r!
Ω	4.6118370899846	Real period
R	0.32705630608246	Regulator
r	2	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33872g1 19053a1 52925d1 103733j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2117a1

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	-2	0	-2	-3	-4	-3	-6	1	-	4	0	-12	-4	-9	0	-14	-10	3	-1	+	8	-2	-12	2

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Quadratic twists for elliptic curve 2117a1

-4	-3	5	-7	29
33872g1	19053a1	52925d1	103733j1	61393b1

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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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