Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2- 11+	Signs for the Atkin-Lehner involutions
Class	704h	Isogeny class
Conductor	704	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-85184 = -1 · 26 · 113	Discriminant
Eigenvalues	2-  3 -1  0 11+  6 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2,14]	[a1,a2,a3,a4,a6]
j	13824/1331	j-invariant
L	2.6129403750058	L(r)(E,1)/r!
Ω	2.6129403750058	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	704l1 352f1 6336cf1 17600ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704h1

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	-1	0	+	6	-4	6	-3	4	9	-7	-2	6	-12	-2	9	-8	-15	3	-6	6	-6	-5	-3

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Quadratic twists for elliptic curve 704h1

-4	8	-3	5	-7	-11	13
704l1	352f1	6336cf1	17600ca1	34496da1	7744bi1	118976dn1

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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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