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	5040n	Isogeny class
Conductor	5040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	8230118400 = 210 · 38 · 52 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-507,506]	[a1,a2,a3,a4,a6]
Generators	[-13:70:1]	Generators of the group modulo torsion
j	19307236/11025	j-invariant
L	3.9886126734322	L(r)(E,1)/r!
Ω	1.123039646001	Real period
R	0.88790558010025	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	2520i2 20160dp2 1680a2 25200bm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040n2

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	-2	-4	0	-2	-4	2	2	-8	-4	2	12	-14	-8	-8	-2	-8	-4	18	-2

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Quadratic twists for elliptic curve 5040n2

-4	8	-3	5	-7
2520i2	20160dp2	1680a2	25200bm2	35280bb2

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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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