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	5040x	Isogeny class
Conductor	5040	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	111002148321361920 = 226 · 39 · 5 · 75	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4  6 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-737883,243438858]	[a1,a2,a3,a4,a6]
Generators	[423:2646:1]	Generators of the group modulo torsion
j	551105805571803/1376829440	j-invariant
L	3.6528721591884	L(r)(E,1)/r!
Ω	0.3344349317519	Real period
R	1.0922519785996	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	630g1 20160dm1 5040bb1 25200ct1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040x1

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

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Quadratic twists for elliptic curve 5040x1

-4	8	-3	5	-7
630g1	20160dm1	5040bb1	25200ct1	35280dp1

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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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