Cremona's table of elliptic curves

6308 = 2² · 19 · 83

Field	Data	Notes
Atkin-Lehner	2- 19+ 83-	Signs for the Atkin-Lehner involutions
Class	6308d	Isogeny class
Conductor	6308	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3744	Modular degree for the optimal curve
Δ	-33508096 = -1 · 28 · 19 · 832	Discriminant
Eigenvalues	2- -2  1  1 -3 -2 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5245,-147969]	[a1,a2,a3,a4,a6]
Generators	[85:166:1]	Generators of the group modulo torsion
j	-62345200132096/130891	j-invariant
L	2.8808031189388	L(r)(E,1)/r!
Ω	0.2804957150823	Real period
R	1.7117332898137	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	25232m1 100928i1 56772c1 119852d1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 6308d1

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	1	1	-3	-2	-3	+	8	8	-2	6	8	3	-3	-12	-12	3	8	8	3	-8	-	0	-8

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Quadratic twists for elliptic curve 6308d1

-4	8	-3	-19
25232m1	100928i1	56772c1	119852d1

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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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