Cremona's table of elliptic curves

6279 = 3 · 7 · 13 · 23

Field	Data	Notes
Atkin-Lehner	3- 7+ 13- 23+	Signs for the Atkin-Lehner involutions
Class	6279j	Isogeny class
Conductor	6279	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-6083578683 = -1 · 33 · 73 · 134 · 23	Discriminant
Eigenvalues	-2 3-  0 7+  3 13-  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2308,42082]	[a1,a2,a3,a4,a6]
Generators	[29:-20:1]	Generators of the group modulo torsion
j	-1360251712000000/6083578683	j-invariant
L	2.5162951253586	L(r)(E,1)/r!
Ω	1.3502726186221	Real period
R	0.15529549926039	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	100464bj1 18837g1 43953i1 81627w1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6279j1

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	-	0	+	3	-	0	-1	+	2	-2	-2	5	0	-9	-11	-7	11	-4	-12	0	-6	6	-14	6

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Quadratic twists for elliptic curve 6279j1

-4	-3	-7	13
100464bj1	18837g1	43953i1	81627w1

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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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