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	6240bc	Isogeny class
Conductor	6240	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-219375000000 = -1 · 26 · 33 · 510 · 13	Discriminant
Eigenvalues	2- 3- 5+  2  0 13+  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1966,-41080]	[a1,a2,a3,a4,a6]
Generators	[61:264:1]	Generators of the group modulo torsion
j	-13137573612736/3427734375	j-invariant
L	4.7504558074547	L(r)(E,1)/r!
Ω	0.35364123578673	Real period
R	4.4776601507707	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	6240v1 12480cg1 18720r1 31200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240bc1

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	+	0	-6	-2	-4	8	-10	-2	-12	-4	6	8	-2	-4	0	0	0	4	-14	-8

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Quadratic twists for elliptic curve 6240bc1

-4	8	-3	5	13
6240v1	12480cg1	18720r1	31200g1	81120w1

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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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