Cremona's table of elliptic curves

7161 = 3 · 7 · 11 · 31

Field	Data	Notes
Atkin-Lehner	3+ 7- 11- 31-	Signs for the Atkin-Lehner involutions
Class	7161f	Isogeny class
Conductor	7161	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-3859779 = -1 · 3 · 73 · 112 · 31	Discriminant
Eigenvalues	2 3+  3 7- 11- -3  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-54,-163]	[a1,a2,a3,a4,a6]
j	-17738739712/3859779	j-invariant
L	5.2147673569446	L(r)(E,1)/r!
Ω	0.86912789282411	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	114576bq1 21483m1 50127q1 78771f1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7161f1

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	+	3	-	-	-3	6	2	7	-3	-	2	5	-4	0	5	0	-5	-3	12	1	-10	8	-4	0

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Quadratic twists for elliptic curve 7161f1

-4	-3	-7	-11
114576bq1	21483m1	50127q1	78771f1

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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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