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	6308c	Isogeny class
Conductor	6308	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	29232	Modular degree for the optimal curve
Δ	-1576417896952576 = -1 · 28 · 197 · 832	Discriminant
Eigenvalues	2-  2 -3  1  1 -4  5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,22643,1381449]	[a1,a2,a3,a4,a6]
Generators	[25848:1088047:729]	Generators of the group modulo torsion
j	5014948370604032/6157882409971	j-invariant
L	4.7779534404252	L(r)(E,1)/r!
Ω	0.31849282621003	Real period
R	7.500880784791	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	25232n1 100928k1 56772e1 119852e1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 6308c1

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	-3	1	1	-4	5	+	4	-6	8	0	-6	-9	1	-6	-12	15	10	2	-9	-2	-	4	-12

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Quadratic twists for elliptic curve 6308c1

-4	8	-3	-19
25232n1	100928k1	56772e1	119852e1

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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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