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	1170h	Isogeny class
Conductor	1170	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-299342238474240000 = -1 · 216 · 39 · 54 · 135	Discriminant
Eigenvalues	2- 3+ 5+  2  4 13+ -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,151252,-13465169]	[a1,a2,a3,a4,a6]
j	19441890357117957/15208161280000	j-invariant
L	2.734885356077	L(r)(E,1)/r!
Ω	0.17093033475481	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9360y1 37440x1 1170a1 5850e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170h1

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

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Quadratic twists for elliptic curve 1170h1

-4	8	-3	5	-7	13
9360y1	37440x1	1170a1	5850e1	57330dm1	15210c1

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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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