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	6348c	Isogeny class
Conductor	6348	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-406272 = -1 · 28 · 3 · 232	Discriminant
Eigenvalues	2- 3+  4 -3  0  1  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-61,-167]	[a1,a2,a3,a4,a6]
Generators	[264:235:27]	Generators of the group modulo torsion
j	-188416/3	j-invariant
L	4.1201712262322	L(r)(E,1)/r!
Ω	0.85218648144472	Real period
R	4.8348234992501	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	25392bg1 101568bu1 19044m1 6348d1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 6348c1

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
-	+	4	-3	0	1	4	-4	-	-8	-8	-11	-8	1	2	10	14	-11	-5	6	-6	-8	-14	-6	14

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Quadratic twists for elliptic curve 6348c1

-4	8	-3	-23
25392bg1	101568bu1	19044m1	6348d1

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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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