Cremona's table of elliptic curves

2116 = 2² · 23²

Field	Data	Notes
Atkin-Lehner	2- 23-	Signs for the Atkin-Lehner involutions
Class	2116a	Isogeny class
Conductor	2116	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	3312	Modular degree for the optimal curve
Δ	-20047612231936 = -1 · 28 · 238	Discriminant
Eigenvalues	2-  0  1  2 -4  1 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12167,-559682]	[a1,a2,a3,a4,a6]
Generators	[219:2698:1]	Generators of the group modulo torsion
j	-9936	j-invariant
L	3.2027806184717	L(r)(E,1)/r!
Ω	0.22599759859355	Real period
R	4.7239154138564	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	8464k1 33856c1 19044i1 52900g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2116a1

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
-	0	1	2	-4	1	-2	-2	-	5	-6	-10	-9	10	-12	5	6	1	8	-6	-9	12	-10	15	15

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Quadratic twists for elliptic curve 2116a1

-4	8	-3	5	-7	-23
8464k1	33856c1	19044i1	52900g1	103684c1	2116b1

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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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