Cremona's table of elliptic curves

61347 = 3 · 11² · 13²

Field	Data	Notes
Atkin-Lehner	3- 11- 13+	Signs for the Atkin-Lehner involutions
Class	61347z	Isogeny class
Conductor	61347	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	1290240	Modular degree for the optimal curve
Δ	-8022732280967445327 = -1 · 38 · 117 · 137	Discriminant
Eigenvalues	-1 3-  2  0 11- 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-491202,-190117773]	[a1,a2,a3,a4,a6]
Generators	[7473:639294:1]	Generators of the group modulo torsion
j	-1532808577/938223	j-invariant
L	5.624249904084	L(r)(E,1)/r!
Ω	0.087723688354967	Real period
R	8.0141550268892	Regulator
r	1	Rank of the group of rational points
S	1.0000000000047	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5577g1 4719j1	Quadratic twists by: -11 13

Hecke Eigenvalues for elliptic curve 61347z1

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	-	2	0	-	+	6	-4	-8	10	0	-6	10	-4	-8	-10	12	-14	12	0	-6	-8	12	-2	14

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Quadratic twists for elliptic curve 61347z1

-11	13
5577g1	4719j1

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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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