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	5278f	Isogeny class
Conductor	5278	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1472	Modular degree for the optimal curve
Δ	-15918448 = -1 · 24 · 7 · 132 · 292	Discriminant
Eigenvalues	2-  2 -2 7- -4 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-14,187]	[a1,a2,a3,a4,a6]
Generators	[11:33:1]	Generators of the group modulo torsion
j	-304821217/15918448	j-invariant
L	6.7843498507026	L(r)(E,1)/r!
Ω	1.8267546077992	Real period
R	0.9284703350052	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42224g1 47502r1 36946t1 68614a1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5278f1

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	-	-4	+	-4	-2	8	+	-2	-2	-12	-4	6	-10	0	-8	4	8	8	0	4	-8	0

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Quadratic twists for elliptic curve 5278f1

-4	-3	-7	13
42224g1	47502r1	36946t1	68614a1

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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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