Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	704k	Isogeny class
Conductor	704	Conductor
∏ cp	5	Product of Tamagawa factors cp
Δ	-10307264 = -1 · 26 · 115	Discriminant
Eigenvalues	2- -1 -1  2 11- -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-41,199]	[a1,a2,a3,a4,a6]
Generators	[2:11:1]	Generators of the group modulo torsion
j	-122023936/161051	j-invariant
L	1.8879135472039	L(r)(E,1)/r!
Ω	2.0630782446897	Real period
R	0.18301909315009	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	704a2 176b2 6336bx2 17600cd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704k2

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	2	-	-4	-2	0	1	0	-7	-3	-8	-6	-8	6	5	-12	-7	3	4	10	-6	15	-7

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Quadratic twists for elliptic curve 704k2

-4	8	-3	5	-7	-11	13
704a2	176b2	6336bx2	17600cd2	34496de2	7744y2	118976cb2

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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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