Cremona's table of elliptic curves

649 = 11 · 59

Field	Data	Notes
Atkin-Lehner	11- 59-	Signs for the Atkin-Lehner involutions
Class	649a	Isogeny class
Conductor	649	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-7139 = -1 · 112 · 59	Discriminant
Eigenvalues	-1  1 -1  1 11- -4 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1,4]	[a1,a2,a3,a4,a6]
Generators	[3:4:1]	Generators of the group modulo torsion
j	-117649/7139	j-invariant
L	1.6065376871376	L(r)(E,1)/r!
Ω	3.4660507042557	Real period
R	0.23175334468781	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	10384c1 41536b1 5841e1 16225d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 649a1

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	1	-1	1	-	-4	-2	-1	6	-9	2	-4	-3	6	-12	-13	-	8	10	0	-4	-1	-6	0	-2

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Quadratic twists for elliptic curve 649a1

-4	8	-3	5	-7	-11	13	-59
10384c1	41536b1	5841e1	16225d1	31801c1	7139e1	109681a1	38291a1

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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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