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	6240k	Isogeny class
Conductor	6240	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	21902400 = 26 · 34 · 52 · 132	Discriminant
Eigenvalues	2+ 3- 5+  4  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-86,-240]	[a1,a2,a3,a4,a6]
j	1111934656/342225	j-invariant
L	3.2076559085618	L(r)(E,1)/r!
Ω	1.6038279542809	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6240b1 12480ci2 18720bm1 31200bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240k1

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
+	-	+	4	4	+	2	-4	0	6	0	10	2	-4	4	-6	-4	-2	-4	-8	-2	16	4	10	-2

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Quadratic twists for elliptic curve 6240k1

-4	8	-3	5	13
6240b1	12480ci2	18720bm1	31200bq1	81120cc1

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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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