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	1170i	Isogeny class
Conductor	1170	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-94910400 = -1 · 26 · 33 · 52 · 133	Discriminant
Eigenvalues	2- 3+ 5+ -4  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,97,-313]	[a1,a2,a3,a4,a6]
Generators	[13:48:1]	Generators of the group modulo torsion
j	3774555693/3515200	j-invariant
L	3.2585381990432	L(r)(E,1)/r!
Ω	1.0398417359845	Real period
R	1.5668433408081	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	9360bb1 37440s1 1170b3 5850b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170i1

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

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Quadratic twists for elliptic curve 1170i1

-4	8	-3	5	-7	13
9360bb1	37440s1	1170b3	5850b1	57330dh1	15210e1

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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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