Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2+ 11-	Signs for the Atkin-Lehner involutions
Class	704c	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]
j	512/11	j-invariant
L	2.4683463701649	L(r)(E,1)/r!
Ω	2.4683463701649	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	704b1 352d1 6336t1 17600p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704c1

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 704c1

-4	8	-3	5	-7	-11	13
704b1	352d1	6336t1	17600p1	34496bo1	7744g1	118976g1

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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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