Cremona's table of elliptic curves

1170 = 2 · 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 13+	Signs for the Atkin-Lehner involutions
Class	1170n	Isogeny class
Conductor	1170	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	-1937784176640 = -1 · 220 · 37 · 5 · 132	Discriminant
Eigenvalues	2- 3- 5-  4  0 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2597,-83491]	[a1,a2,a3,a4,a6]
j	-2656166199049/2658140160	j-invariant
L	3.2142459329827	L(r)(E,1)/r!
Ω	0.32142459329827	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	9360bz1 37440bv1 390g1 5850r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170n1

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

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Quadratic twists for elliptic curve 1170n1

-4	8	-3	5	-7	13
9360bz1	37440bv1	390g1	5850r1	57330eg1	15210o1

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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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