Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2- 11+	Signs for the Atkin-Lehner involutions
Class	704g	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]
j	-2515456/11	j-invariant
L	1.3006681579663	L(r)(E,1)/r!
Ω	1.3006681579663	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	704j1 352a1 6336cg1 17600bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704g1

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 704g1

-4	8	-3	5	-7	-11	13
704j1	352a1	6336cg1	17600bq1	34496ck1	7744z1	118976cy1

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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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