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	5040bm	Isogeny class
Conductor	5040	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	1743790781250000 = 24 · 313 · 510 · 7	Discriminant
Eigenvalues	2- 3- 5- 7-  2  4 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-36552,1788379]	[a1,a2,a3,a4,a6]
Generators	[1553:60750:1]	Generators of the group modulo torsion
j	463030539649024/149501953125	j-invariant
L	4.278027987031	L(r)(E,1)/r!
Ω	0.43533257496529	Real period
R	0.98270339346237	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	1260h1 20160ed1 1680q1 25200dv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bm1

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

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Quadratic twists for elliptic curve 5040bm1

-4	8	-3	5	-7
1260h1	20160ed1	1680q1	25200dv1	35280ef1

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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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