Cremona's table of elliptic curves

2116 = 2² · 23²

Field	Data	Notes
Atkin-Lehner	2- 23-	Signs for the Atkin-Lehner involutions
Class	2116d	Isogeny class
Conductor	2116	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3168	Modular degree for the optimal curve
Δ	-54477207152 = -1 · 24 · 237	Discriminant
Eigenvalues	2- -3  2  4 -2 -5 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-529,-12167]	[a1,a2,a3,a4,a6]
Generators	[69:529:1]	Generators of the group modulo torsion
j	-6912/23	j-invariant
L	2.3424211051056	L(r)(E,1)/r!
Ω	0.45801922762389	Real period
R	0.85237364278991	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	8464q1 33856t1 19044k1 52900u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2116d1

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
-	-3	2	4	-2	-5	-4	2	-	-7	-3	-2	-9	8	9	-2	0	2	-14	-3	-3	6	-8	-12	0

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Quadratic twists for elliptic curve 2116d1

-4	8	-3	5	-7	-23
8464q1	33856t1	19044k1	52900u1	103684j1	92b1

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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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