Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	704j	Isogeny class
Conductor	704	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-704 = -1 · 26 · 11	Discriminant
Eigenvalues	2-  1 -1 -4 11-  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11,11]	[a1,a2,a3,a4,a6]
Generators	[2:1:1]	Generators of the group modulo torsion
j	-2515456/11	j-invariant
L	2.249086577795	L(r)(E,1)/r!
Ω	5.110323666644	Real period
R	0.44010648336723	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	704g1 352c1 6336by1 17600ci1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704j1

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	-4	-	2	0	-2	-9	-4	-5	9	2	-6	4	6	-5	0	-13	1	14	10	14	-13	-19

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Quadratic twists for elliptic curve 704j1

-4	8	-3	5	-7	-11	13
704g1	352c1	6336by1	17600ci1	34496dh1	7744w1	118976bx1

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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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