Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2- 11+	Signs for the Atkin-Lehner involutions
Class	704i	Isogeny class
Conductor	704	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-180224 = -1 · 214 · 11	Discriminant
Eigenvalues	2- -3  3  2 11+  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16,-32]	[a1,a2,a3,a4,a6]
j	-27648/11	j-invariant
L	1.1705612908875	L(r)(E,1)/r!
Ω	1.1705612908875	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	704e1 176a1 6336cl1 17600bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704i1

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
-	-3	3	2	+	0	-6	4	-1	8	7	1	4	6	8	-2	-1	-4	-5	-3	16	-2	-2	15	-7

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Quadratic twists for elliptic curve 704i1

-4	8	-3	5	-7	-11	13
704e1	176a1	6336cl1	17600bz1	34496cy1	7744bk1	118976do1

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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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