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	6240c	Isogeny class
Conductor	6240	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	2433600 = 26 · 32 · 52 · 132	Discriminant
Eigenvalues	2+ 3+ 5+  0  4 13-  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-46,-80]	[a1,a2,a3,a4,a6]
j	171879616/38025	j-invariant
L	1.8587763378297	L(r)(E,1)/r!
Ω	1.8587763378297	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	6240m1 12480cv2 18720br1 31200bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240c1

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 6240c1

-4	8	-3	5	13
6240m1	12480cv2	18720br1	31200bu1	81120bj1

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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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