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	12716d	Isogeny class
Conductor	12716	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-8224538710784 = -1 · 28 · 113 · 176	Discriminant
Eigenvalues	2- -1  3 -2 11- -4 17+  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-22349,-1285943]	[a1,a2,a3,a4,a6]
Generators	[584:13583:1]	Generators of the group modulo torsion
j	-199794688/1331	j-invariant
L	4.3022063960663	L(r)(E,1)/r!
Ω	0.19515539029008	Real period
R	3.6741716346065	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	50864bd2 114444i2 44a2	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 12716d2

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
-	-1	3	-2	-	-4	+	8	3	0	-5	1	0	-10	0	-6	3	4	-1	-15	4	-2	6	-9	7

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Quadratic twists for elliptic curve 12716d2

-4	-3	17
50864bd2	114444i2	44a2

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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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