Cremona's table of elliptic curves

2670 = 2 · 3 · 5 · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 89-	Signs for the Atkin-Lehner involutions
Class	2670f	Isogeny class
Conductor	2670	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	1829563747560 = 23 · 36 · 5 · 894	Discriminant
Eigenvalues	2- 3- 5- -4 -4 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-155685,-23656743]	[a1,a2,a3,a4,a6]
Generators	[-228:123:1]	Generators of the group modulo torsion
j	417315196209220773841/1829563747560	j-invariant
L	5.084388736903	L(r)(E,1)/r!
Ω	0.24034658824678	Real period
R	1.1752446456574	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	21360k4 85440e4 8010c3 13350b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2670f3

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

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Quadratic twists for elliptic curve 2670f3

-4	8	-3	5
21360k4	85440e4	8010c3	13350b3

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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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