Cremona's table of elliptic curves

80613 = 3² · 13² · 53

Field	Data	Notes
Atkin-Lehner	3+ 13+ 53-	Signs for the Atkin-Lehner involutions
Class	80613f	Isogeny class
Conductor	80613	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	166656	Modular degree for the optimal curve
Δ	-89793127827 = -1 · 33 · 137 · 53	Discriminant
Eigenvalues	2 3+  4  4 -1 13+  2  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,507,13731]	[a1,a2,a3,a4,a6]
j	110592/689	j-invariant
L	12.444325268348	L(r)(E,1)/r!
Ω	0.77777033051421	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	80613c1 6201b1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 80613f1

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	+	4	4	-1	+	2	5	3	0	8	0	8	-9	0	-	9	-14	5	-6	-2	8	0	10	14

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Quadratic twists for elliptic curve 80613f1

-3	13
80613c1	6201b1

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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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