Cremona's table of elliptic curves

12922 = 2 · 7 · 13 · 71

Field	Data	Notes
Atkin-Lehner	2- 7- 13- 71-	Signs for the Atkin-Lehner involutions
Class	12922f	Isogeny class
Conductor	12922	Conductor
∏ cp	750	Product of Tamagawa factors cp
deg	228000	Modular degree for the optimal curve
Δ	-1030798063517401088 = -1 · 215 · 75 · 135 · 712	Discriminant
Eigenvalues	2- -1 -4 7- -3 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,179935,39101151]	[a1,a2,a3,a4,a6]
Generators	[51:6932:1]	Generators of the group modulo torsion
j	644273852242214179439/1030798063517401088	j-invariant
L	3.9590884408159	L(r)(E,1)/r!
Ω	0.18889363899103	Real period
R	0.69864509677921	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	103376k1 116298s1 90454l1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12922f1

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	-4	-	-3	-	-2	0	-1	0	7	3	-3	-6	3	4	0	7	13	-	-1	15	-6	-10	-17

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Quadratic twists for elliptic curve 12922f1

-4	-3	-7
103376k1	116298s1	90454l1

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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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