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	2170j	Isogeny class
Conductor	2170	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-1831121689600 = -1 · 210 · 52 · 74 · 313	Discriminant
Eigenvalues	2-  0 5+ 7+ -2  6 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1993,74057]	[a1,a2,a3,a4,a6]
Generators	[-37:328:1]	Generators of the group modulo torsion
j	-875066990644449/1831121689600	j-invariant
L	4.0405433235078	L(r)(E,1)/r!
Ω	0.74247074481375	Real period
R	0.18140078702232	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	17360w1 69440bp1 19530x1 10850n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2170j1

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	+	+	-2	6	-4	0	-6	0	-	-10	-10	4	-4	-2	-8	-8	-12	8	-4	16	-4	-14	14

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Quadratic twists for elliptic curve 2170j1

-4	8	-3	5	-7	-31
17360w1	69440bp1	19530x1	10850n1	15190bc1	67270w1

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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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