Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2+ 11+	Signs for the Atkin-Lehner involutions
Class	704a	Isogeny class
Conductor	704	Conductor
∏ cp	1	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	[8:7:1]	Generators of the group modulo torsion
j	-122023936/161051	j-invariant
L	2.2759885634581	L(r)(E,1)/r!
Ω	0.89746650580113	Real period
R	2.5360150476329	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	704k2 11a1 6336y2 17600e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704a2

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 704a2

-4	8	-3	5	-7	-11	13
704k2	11a1	6336y2	17600e2	34496p2	7744f2	118976bb2

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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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