Cremona's table of elliptic curves

7440 = 2⁴ · 3 · 5 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 31-	Signs for the Atkin-Lehner involutions
Class	7440ba	Isogeny class
Conductor	7440	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-1153200 = -1 · 24 · 3 · 52 · 312	Discriminant
Eigenvalues	2- 3- 5-  0  0 -2 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,15,-42]	[a1,a2,a3,a4,a6]
Generators	[1542:11780:27]	Generators of the group modulo torsion
j	21807104/72075	j-invariant
L	5.2731917805954	L(r)(E,1)/r!
Ω	1.4006378256361	Real period
R	3.7648503303846	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	1860a1 29760bt1 22320bm1 37200bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7440ba1

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

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Quadratic twists for elliptic curve 7440ba1

-4	8	-3	5
1860a1	29760bt1	22320bm1	37200bt1

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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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