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	3800243261880 = 23 · 39 · 5 · 136	Discriminant
Eigenvalues	2+ 3+ 5- -4  0 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4524,71288]	[a1,a2,a3,a4,a6]
Generators	[-71:211:1]	Generators of the group modulo torsion
j	520300455507/193072360	j-invariant
L	1.9272332668144	L(r)(E,1)/r!
Ω	0.71814555761064	Real period
R	0.89454161782402	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	9360bh4 37440e4 1170i2 5850bd4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170b4

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 1170b4

-4	8	-3	5	-7	13
9360bh4	37440e4	1170i2	5850bd4	57330c4	15210ba4

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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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