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	1170f	Isogeny class
Conductor	1170	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	7581600000 = 28 · 36 · 55 · 13	Discriminant
Eigenvalues	2+ 3- 5- -4  2 13+ -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-7569,255325]	[a1,a2,a3,a4,a6]
Generators	[41:92:1]	Generators of the group modulo torsion
j	65787589563409/10400000	j-invariant
L	1.9319063230081	L(r)(E,1)/r!
Ω	1.2757152772817	Real period
R	0.30287421612206	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9360by1 37440bx1 130c1 5850bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170f1

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

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Quadratic twists for elliptic curve 1170f1

-4	8	-3	5	-7	13
9360by1	37440bx1	130c1	5850bt1	57330bk1	15210bj1

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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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