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	6240m	Isogeny class
Conductor	6240	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	99840000 = 212 · 3 · 54 · 13	Discriminant
Eigenvalues	2+ 3- 5+  0 -4 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-241,-1441]	[a1,a2,a3,a4,a6]
Generators	[-70:69:8]	Generators of the group modulo torsion
j	379503424/24375	j-invariant
L	4.4359414040499	L(r)(E,1)/r!
Ω	1.2161619393325	Real period
R	3.6474923779349	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	6240c3 12480cb1 18720bp3 31200be3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240m2

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

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Quadratic twists for elliptic curve 6240m2

-4	8	-3	5	13
6240c3	12480cb1	18720bp3	31200be3	81120bv3

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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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