Cremona's table of elliptic curves

12716 = 2² · 11 · 17²

Field	Data	Notes
Atkin-Lehner	2- 11- 17+	Signs for the Atkin-Lehner involutions
Class	12716f	Isogeny class
Conductor	12716	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	110592	Modular degree for the optimal curve
Δ	-19643732953856 = -1 · 28 · 11 · 178	Discriminant
Eigenvalues	2- -3 -3  2 11- -2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-143344,-20890076]	[a1,a2,a3,a4,a6]
Generators	[612:10982:1]	Generators of the group modulo torsion
j	-52714340352/3179	j-invariant
L	2.1822743289914	L(r)(E,1)/r!
Ω	0.12267981370774	Real period
R	2.9647288920059	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	50864bh1 114444g1 748a1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 12716f1

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	-3	2	-	-2	+	2	-3	10	-7	7	-4	2	0	-10	-5	0	-9	7	-14	-4	18	-9	17

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Quadratic twists for elliptic curve 12716f1

-4	-3	17
50864bh1	114444g1	748a1

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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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