Cremona's table of elliptic curves

7140 = 2² · 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	7140j	Isogeny class
Conductor	7140	Conductor
∏ cp	324	Product of Tamagawa factors cp
deg	62208	Modular degree for the optimal curve
Δ	186532892520786000 = 24 · 318 · 53 · 72 · 173	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -4 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-158781,-12751956]	[a1,a2,a3,a4,a6]
Generators	[-165:2997:1]	Generators of the group modulo torsion
j	27669547892867989504/11658305782549125	j-invariant
L	4.7091392141574	L(r)(E,1)/r!
Ω	0.24833428276682	Real period
R	2.1069893557679	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	28560cj1 114240ck1 21420w1 35700a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7140j1

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

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Quadratic twists for elliptic curve 7140j1

-4	8	-3	5	-7	17
28560cj1	114240ck1	21420w1	35700a1	49980j1	121380m1

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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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