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	2170n	Isogeny class
Conductor	2170	Conductor
∏ cp	144	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-149479321600 = -1 · 212 · 52 · 72 · 313	Discriminant
Eigenvalues	2- -2 5+ 7-  6  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-126,-18620]	[a1,a2,a3,a4,a6]
j	-221335335649/149479321600	j-invariant
L	1.8525296357428	L(r)(E,1)/r!
Ω	0.46313240893569	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	17360s1 69440ca1 19530bh1 10850i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2170n1

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

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Quadratic twists for elliptic curve 2170n1

-4	8	-3	5	-7	-31
17360s1	69440ca1	19530bh1	10850i1	15190be1	67270bg1

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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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