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	6240ba	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	[21:90:1]	Generators of the group modulo torsion
j	504358336/38025	j-invariant
L	4.5513263044284	L(r)(E,1)/r!
Ω	1.6808628335732	Real period
R	2.7077321322842	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	6240a1 12480o2 18720n1 31200d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240ba1

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 6240ba1

-4	8	-3	5	13
6240a1	12480o2	18720n1	31200d1	81120u1

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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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