Cremona's table of elliptic curves

8281 = 7² · 13²

Field	Data	Notes
Atkin-Lehner	7+ 13+	Signs for the Atkin-Lehner involutions
Class	8281a	Isogeny class
Conductor	8281	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	72072	Modular degree for the optimal curve
Δ	4702525276151521 = 78 · 138	Discriminant
Eigenvalues	1 -3  3 7+ -3 13+ -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-47098,-2131193]	[a1,a2,a3,a4,a6]
Generators	[-250338:414193:1331]	Generators of the group modulo torsion
j	2457	j-invariant
L	3.4579790233581	L(r)(E,1)/r!
Ω	0.33580582196997	Real period
R	10.297555304647	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	74529o1 8281e1 8281c1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 8281a1

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
1	-3	3	+	-3	+	-2	-1	0	7	3	2	3	-7	1	3	-4	-13	-3	13	-13	-3	0	6	-5

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Quadratic twists for elliptic curve 8281a1

-3	-7	13
74529o1	8281e1	8281c1

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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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