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	5040f	Isogeny class
Conductor	5040	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	45378900000000 = 28 · 33 · 58 · 75	Discriminant
Eigenvalues	2+ 3+ 5- 7-  2 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-268287,53485934]	[a1,a2,a3,a4,a6]
Generators	[173:-3500:1]	Generators of the group modulo torsion
j	308971819397054448/6565234375	j-invariant
L	4.1527514697151	L(r)(E,1)/r!
Ω	0.58983708587145	Real period
R	0.17601264693198	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	2520b2 20160cx2 5040c2 25200c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040f2

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
+	+	-	-	2	-6	2	-4	-2	0	-4	10	-10	-12	-12	4	-4	6	4	2	6	-8	-16	-18	6

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Quadratic twists for elliptic curve 5040f2

-4	8	-3	5	-7
2520b2	20160cx2	5040c2	25200c2	35280e2

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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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