Cremona's table of elliptic curves

3111 = 3 · 17 · 61

Field	Data	Notes
Atkin-Lehner	3+ 17+ 61+	Signs for the Atkin-Lehner involutions
Class	3111a	Isogeny class
Conductor	3111	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	-1707939 = -1 · 33 · 17 · 612	Discriminant
Eigenvalues	2 3+ -1 -2  3  3 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-6,65]	[a1,a2,a3,a4,a6]
Generators	[10:57:8]	Generators of the group modulo torsion
j	-28094464/1707939	j-invariant
L	5.1233559389129	L(r)(E,1)/r!
Ω	2.1957770339119	Real period
R	1.1666384746236	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	49776m1 9333a1 77775h1 52887d1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3111a1

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
2	+	-1	-2	3	3	+	-1	3	-6	-4	4	-3	-1	-6	-12	8	+	-12	4	14	-6	-16	-8	-2

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Quadratic twists for elliptic curve 3111a1

-4	-3	5	17
49776m1	9333a1	77775h1	52887d1

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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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