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	24	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-21937500 = -1 · 22 · 33 · 56 · 13	Discriminant
Eigenvalues	2+ 3+ 5- -4  0 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-249,1593]	[a1,a2,a3,a4,a6]
Generators	[-8:59:1]	Generators of the group modulo torsion
j	-63378025803/812500	j-invariant
L	1.9272332668144	L(r)(E,1)/r!
Ω	2.1544366728319	Real period
R	1.341812426736	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	9360bh1 37440e1 1170i3 5850bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170b1

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 1170b1

-4	8	-3	5	-7	13
9360bh1	37440e1	1170i3	5850bd1	57330c1	15210ba1

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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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