Cremona's table of elliptic curves

611 = 13 · 47

Field	Data	Notes
Atkin-Lehner	13- 47+	Signs for the Atkin-Lehner involutions
Conductor	611	Conductor
Count	1	Number of curves in isogeny class
Curves	611a1	Curves in isogeny class
deg	58	Modular degree for the optimal curve
Eigenvalues	2  3 -2  2 -3 13-  3 -4	Hecke eigenvalues for primes less than 20
L	4.4507748026432	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	9776d 39104b 5499j 15275d	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 611a

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 isogeny class 611a

-4	8	-3	5	-7	-11	13	-47
9776d	39104b	5499j	15275d	29939c	73931c	7943c	28717a

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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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