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	60	Product of Tamagawa factors cp
Δ	6958028859040 = 25 · 5 · 72 · 316	Discriminant
Eigenvalues	2-  0 5+ 7+ -2  6 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-41193,3225737]	[a1,a2,a3,a4,a6]
Generators	[107:132:1]	Generators of the group modulo torsion
j	7730081871906369249/6958028859040	j-invariant
L	4.0405433235078	L(r)(E,1)/r!
Ω	0.74247074481375	Real period
R	0.36280157404464	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	17360w2 69440bp2 19530x2 10850n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2170j2

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 2170j2

-4	8	-3	5	-7	-31
17360w2	69440bp2	19530x2	10850n2	15190bc2	67270w2

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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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