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	5040h	Isogeny class
Conductor	5040	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	967680 = 210 · 33 · 5 · 7	Discriminant
Eigenvalues	2+ 3+ 5- 7- -4  6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27,26]	[a1,a2,a3,a4,a6]
Generators	[-5:6:1]	Generators of the group modulo torsion
j	78732/35	j-invariant
L	4.1609389800014	L(r)(E,1)/r!
Ω	2.5030384253051	Real period
R	0.83117760756992	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	2520c1 20160cy1 5040d1 25200j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040h1

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	2	-8	-6	-4	-8	2	-6	6	-2	-4	0	-14	2	6	-8	8	-6	18

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Quadratic twists for elliptic curve 5040h1

-4	8	-3	5	-7
2520c1	20160cy1	5040d1	25200j1	35280i1

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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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