Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2+ 11+	Signs for the Atkin-Lehner involutions
Class	704b	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  3 -4 11+  2 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	512/11	j-invariant
L	2.008608873501	L(r)(E,1)/r!
Ω	3.8045730057765	Real period
R	0.52794594043835	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	704c1 352b1 6336be1 17600c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704b1

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	3	-4	+	2	-8	-6	5	-4	1	-3	-6	6	-12	6	-3	0	-11	-5	-10	-2	2	-5	13

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Quadratic twists for elliptic curve 704b1

-4	8	-3	5	-7	-11	13
704c1	352b1	6336be1	17600c1	34496o1	7744i1	118976bh1

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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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