Cremona's table of elliptic curves

6348 = 2² · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	6348b	Isogeny class
Conductor	6348	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	132480	Modular degree for the optimal curve
Δ	-6.9580631058624E+19	Discriminant
Eigenvalues	2- 3+ -1  2  0  1 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1026084,31601304]	[a1,a2,a3,a4,a6]
Generators	[2310:121338:1]	Generators of the group modulo torsion
j	11265584/6561	j-invariant
L	3.4234704089796	L(r)(E,1)/r!
Ω	0.11768249563153	Real period
R	4.8484559953855	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	25392bb1 101568s1 19044g1 6348a1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 6348b1

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	0	1	-6	6	-	-3	2	-6	7	6	-8	-5	-6	-1	0	6	-1	12	-14	9	9

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Quadratic twists for elliptic curve 6348b1

-4	8	-3	-23
25392bb1	101568s1	19044g1	6348a1

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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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