Cremona's table of elliptic curves

5278 = 2 · 7 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 13- 29+	Signs for the Atkin-Lehner involutions
Class	5278d	Isogeny class
Conductor	5278	Conductor
∏ cp	66	Product of Tamagawa factors cp
deg	7920	Modular degree for the optimal curve
Δ	-1297926576128 = -1 · 211 · 73 · 133 · 292	Discriminant
Eigenvalues	2- -1 -2 7+  3 13- -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2576,-20655]	[a1,a2,a3,a4,a6]
Generators	[125:-1571:1]	Generators of the group modulo torsion
j	1890387126561023/1297926576128	j-invariant
L	4.139949634304	L(r)(E,1)/r!
Ω	0.48646232834853	Real period
R	0.12894422847421	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	42224n1 47502m1 36946o1 68614f1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5278d1

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	-2	+	3	-	-4	6	1	+	3	-1	-7	-8	7	-14	12	1	9	-4	1	-3	16	-10	-5

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Quadratic twists for elliptic curve 5278d1

-4	-3	-7	13
42224n1	47502m1	36946o1	68614f1

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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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