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	6240d	Isogeny class
Conductor	6240	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	12300387840000 = 212 · 37 · 54 · 133	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-25625841,49938972705]	[a1,a2,a3,a4,a6]
j	454357982636417669333824/3003024375	j-invariant
L	1.0460643600644	L(r)(E,1)/r!
Ω	0.34868812002145	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6240l2 12480cu1 18720bo2 31200bv4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240d3

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	-	-2	4	8	-6	0	-10	6	-4	0	6	12	-10	-12	-12	-10	8	16	14	-2

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Quadratic twists for elliptic curve 6240d3

-4	8	-3	5	13
6240l2	12480cu1	18720bo2	31200bv4	81120bh4

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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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