Cremona's table of elliptic curves

611 = 13 · 47

Field	Data	Notes
Atkin-Lehner	13- 47+	Signs for the Atkin-Lehner involutions
Class	611a	Isogeny class
Conductor	611	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	58	Modular degree for the optimal curve
Δ	-611 = -1 · 13 · 47	Discriminant
Eigenvalues	2  3 -2  2 -3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1,1]	[a1,a2,a3,a4,a6]
j	-110592/611	j-invariant
L	4.4507748026432	L(r)(E,1)/r!
Ω	4.4507748026432	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	9776d1 39104b1 5499j1 15275d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 611a1

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	-2	2	-3	-	3	-4	-4	4	-5	8	7	-2	+	9	-14	6	3	-8	9	3	-18	-6	4

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Quadratic twists for elliptic curve 611a1

-4	8	-3	5	-7	-11	13	-47
9776d1	39104b1	5499j1	15275d1	29939c1	73931c1	7943c1	28717a1

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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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