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	36	Product of Tamagawa factors cp
Δ	5212953720 = 23 · 33 · 5 · 136	Discriminant
Eigenvalues	2- 3+ 5+ -4  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-503,-2473]	[a1,a2,a3,a4,a6]
Generators	[25:-2:1]	Generators of the group modulo torsion
j	520300455507/193072360	j-invariant
L	3.2585381990432	L(r)(E,1)/r!
Ω	1.0398417359845	Real period
R	3.1336866816162	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	9360bb2 37440s2 1170b4 5850b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170i2

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 1170i2

-4	8	-3	5	-7	13
9360bb2	37440s2	1170b4	5850b2	57330dh2	15210e2

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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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