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	1170b	Isogeny class
Conductor	1170	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	1140750 = 2 · 33 · 53 · 132	Discriminant
Eigenvalues	2+ 3+ 5- -4  0 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3999,98343]	[a1,a2,a3,a4,a6]
Generators	[-51:435:1]	Generators of the group modulo torsion
j	261984288445803/42250	j-invariant
L	1.9272332668144	L(r)(E,1)/r!
Ω	2.1544366728319	Real period
R	2.683624853472	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	9360bh2 37440e2 1170i4 5850bd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170b2

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 1170b2

-4	8	-3	5	-7	13
9360bh2	37440e2	1170i4	5850bd2	57330c2	15210ba2

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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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