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	2170k	Isogeny class
Conductor	2170	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	8680 = 23 · 5 · 7 · 31	Discriminant
Eigenvalues	2-  1 5+ 7- -5 -5  0  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6,-4]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	24137569/8680	j-invariant
L	4.639323115647	L(r)(E,1)/r!
Ω	3.1388768747218	Real period
R	0.49267336702592	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17360u1 69440bt1 19530bc1 10850a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2170k1

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
-	1	+	-	-5	-5	0	1	-7	-2	+	4	-6	8	-1	-6	1	-4	4	-1	0	0	3	9	3

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Quadratic twists for elliptic curve 2170k1

-4	8	-3	5	-7	-31
17360u1	69440bt1	19530bc1	10850a1	15190bk1	67270be1

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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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