Cremona's table of elliptic curves

12775 = 5² · 7 · 73

Field	Data	Notes
Atkin-Lehner	5- 7+ 73-	Signs for the Atkin-Lehner involutions
Class	12775k	Isogeny class
Conductor	12775	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-4662875 = -1 · 53 · 7 · 732	Discriminant
Eigenvalues	0 -1 5- 7+  3 -7 -1  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-43,-137]	[a1,a2,a3,a4,a6]
Generators	[13:36:1]	Generators of the group modulo torsion
j	-71991296/37303	j-invariant
L	2.4443491644319	L(r)(E,1)/r!
Ω	0.90822310998274	Real period
R	0.67283829754079	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	114975bh1 12775l1 89425bc1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12775k1

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	-1	-	+	3	-7	-1	2	6	-7	-8	8	-6	-6	1	8	14	2	-4	-8	-	-1	12	2	-3

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Quadratic twists for elliptic curve 12775k1

-3	5	-7
114975bh1	12775l1	89425bc1

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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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