Cremona's table of elliptic curves

12635 = 5 · 7 · 19²

Field	Data	Notes
Atkin-Lehner	5- 7- 19-	Signs for the Atkin-Lehner involutions
Class	12635j	Isogeny class
Conductor	12635	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	108345125 = 53 · 74 · 192	Discriminant
Eigenvalues	-2 -2 5- 7- -5  0 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-120,-126]	[a1,a2,a3,a4,a6]
Generators	[-9:17:1] [-7:20:1]	Generators of the group modulo torsion
j	533794816/300125	j-invariant
L	2.7457250921658	L(r)(E,1)/r!
Ω	1.5509359059996	Real period
R	0.14753054814318	Regulator
r	2	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	113715y1 63175j1 88445z1 12635d1	Quadratic twists by: -3 5 -7 -19

Hecke Eigenvalues for elliptic curve 12635j1

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
-2	-2	-	-	-5	0	-4	-	-6	-9	3	2	-2	-10	-8	6	-5	-11	-8	-13	-2	3	-18	-13	-10

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Quadratic twists for elliptic curve 12635j1

-3	5	-7	-19
113715y1	63175j1	88445z1	12635d1

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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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