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	2170d	Isogeny class
Conductor	2170	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	1701280 = 25 · 5 · 73 · 31	Discriminant
Eigenvalues	2+  3 5- 7+ -1 -1  6  3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-124,560]	[a1,a2,a3,a4,a6]
j	211815318681/1701280	j-invariant
L	2.6703213569144	L(r)(E,1)/r!
Ω	2.6703213569144	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17360bn1 69440f1 19530bo1 10850z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2170d1

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
+	3	-	+	-1	-1	6	3	-1	2	+	2	0	4	3	-8	-5	-4	4	9	8	6	13	-9	1

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Quadratic twists for elliptic curve 2170d1

-4	8	-3	5	-7	-31
17360bn1	69440f1	19530bo1	10850z1	15190k1	67270o1

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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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