Cremona's table of elliptic curves

5040 = 2⁴ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	5040bc	Isogeny class
Conductor	5040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	323756265937305600 = 224 · 38 · 52 · 76	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3161163,-2163135238]	[a1,a2,a3,a4,a6]
Generators	[-1359523:407862:1331]	Generators of the group modulo torsion
j	1169975873419524361/108425318400	j-invariant
L	3.5435573885183	L(r)(E,1)/r!
Ω	0.11322445714842	Real period
R	7.8241871892423	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	630i6 20160en6 1680m6 25200eg6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bc6

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

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Quadratic twists for elliptic curve 5040bc6

-4	8	-3	5	-7
630i6	20160en6	1680m6	25200eg6	35280fe6

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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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