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	5040bf	Isogeny class
Conductor	5040	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-163296000 = -1 · 28 · 36 · 53 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+  3 -1  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-48,-628]	[a1,a2,a3,a4,a6]
Generators	[14:38:1]	Generators of the group modulo torsion
j	-65536/875	j-invariant
L	3.5852692807722	L(r)(E,1)/r!
Ω	0.77613285727882	Real period
R	2.3097007472035	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1260g1 20160er1 560f1 25200em1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bf1

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
-	-	+	+	3	-1	3	-2	-6	9	-8	-10	0	-2	-3	0	12	8	-8	0	14	-5	-12	-12	17

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Quadratic twists for elliptic curve 5040bf1

-4	8	-3	5	-7
1260g1	20160er1	560f1	25200em1	35280fo1

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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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