Cremona's table of elliptic curves

6380 = 2² · 5 · 11 · 29

Field	Data	Notes
Atkin-Lehner	2- 5+ 11+ 29-	Signs for the Atkin-Lehner involutions
Class	6380a	Isogeny class
Conductor	6380	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3264	Modular degree for the optimal curve
Δ	985046480 = 24 · 5 · 114 · 292	Discriminant
Eigenvalues	2- -2 5+  2 11+ -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1361,18820]	[a1,a2,a3,a4,a6]
Generators	[4:116:1]	Generators of the group modulo torsion
j	17438019764224/61565405	j-invariant
L	2.623346572313	L(r)(E,1)/r!
Ω	1.570413435664	Real period
R	1.6704814877007	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	25520o1 102080u1 57420p1 31900a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6380a1

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

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Quadratic twists for elliptic curve 6380a1

-4	8	-3	5	-11
25520o1	102080u1	57420p1	31900a1	70180g1

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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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