Cremona's table of elliptic curves

2170 = 2 · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 31+	Signs for the Atkin-Lehner involutions
Class	2170l	Isogeny class
Conductor	2170	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	70911664140800 = 29 · 52 · 78 · 312	Discriminant
Eigenvalues	2- -2 5+ 7- -2  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-66716,6614800]	[a1,a2,a3,a4,a6]
Generators	[58:1686:1]	Generators of the group modulo torsion
j	32840829570040809409/70911664140800	j-invariant
L	3.1778682074544	L(r)(E,1)/r!
Ω	0.61678517755813	Real period
R	0.071559855915485	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	17360v2 69440bu2 19530bb2 10850c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2170l2

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
-	-2	+	-	-2	4	-6	4	-4	-8	+	4	6	-10	8	-12	-8	-4	4	-16	6	-12	-6	-6	-18

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Quadratic twists for elliptic curve 2170l2

-4	8	-3	5	-7	-31
17360v2	69440bu2	19530bb2	10850c2	15190bl2	67270bf2

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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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