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	7161b	Isogeny class
Conductor	7161	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	13120	Modular degree for the optimal curve
Δ	-72746672691 = -1 · 3 · 7 · 112 · 315	Discriminant
Eigenvalues	2 3+ -3 7+ 11-  7 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1772,32105]	[a1,a2,a3,a4,a6]
j	-615686922293248/72746672691	j-invariant
L	2.1232289929396	L(r)(E,1)/r!
Ω	1.0616144964698	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	114576cg1 21483i1 50127t1 78771j1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7161b1

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	+	-	7	-4	2	-1	-3	+	-4	-9	-2	4	5	4	1	1	-4	11	2	14	6	8

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Quadratic twists for elliptic curve 7161b1

-4	-3	-7	-11
114576cg1	21483i1	50127t1	78771j1

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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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