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	7140h	Isogeny class
Conductor	7140	Conductor
∏ cp	240	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	91072931250000 = 24 · 3 · 58 · 75 · 172	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 -2 17-  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13265,371850]	[a1,a2,a3,a4,a6]
Generators	[-95:875:1]	Generators of the group modulo torsion
j	16134601070166016/5692058203125	j-invariant
L	3.7124147878527	L(r)(E,1)/r!
Ω	0.55327436049538	Real period
R	0.11183164125326	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	28560du1 114240dx1 21420p1 35700bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7140h1

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

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Quadratic twists for elliptic curve 7140h1

-4	8	-3	5	-7	17
28560du1	114240dx1	21420p1	35700bc1	49980u1	121380y1

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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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