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	12716b	Isogeny class
Conductor	12716	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	25704	Modular degree for the optimal curve
Δ	-19643732953856 = -1 · 28 · 11 · 178	Discriminant
Eigenvalues	2-  0 -3 -2 11+ -2 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39304,3006756]	[a1,a2,a3,a4,a6]
Generators	[0:1734:1]	Generators of the group modulo torsion
j	-3760128/11	j-invariant
L	2.7937608533218	L(r)(E,1)/r!
Ω	0.68761980509242	Real period
R	0.45143823707869	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	50864br1 114444t1 12716c1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 12716b1

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	-3	-2	+	-2	-	2	3	8	1	2	-2	-4	-9	2	4	6	3	-1	8	4	0	-9	13

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Quadratic twists for elliptic curve 12716b1

-4	-3	17
50864br1	114444t1	12716c1

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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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