Cremona's table of elliptic curves

6240 = 2⁵ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	6240a	Isogeny class
Conductor	6240	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	2433600 = 26 · 32 · 52 · 132	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-66,216]	[a1,a2,a3,a4,a6]
Generators	[-4:20:1]	Generators of the group modulo torsion
j	504358336/38025	j-invariant
L	3.1380764817172	L(r)(E,1)/r!
Ω	2.5237083687934	Real period
R	1.2434386320229	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6240ba1 12480bh2 18720bj1 31200cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240a1

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

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Quadratic twists for elliptic curve 6240a1

-4	8	-3	5	13
6240ba1	12480bh2	18720bj1	31200cb1	81120bg1

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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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