Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2+ 11-	Signs for the Atkin-Lehner involutions
Class	704d	Isogeny class
Conductor	704	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-21807104 = -1 · 214 · 113	Discriminant
Eigenvalues	2+ -1  3  2 11-  4  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-309,-2003]	[a1,a2,a3,a4,a6]
j	-199794688/1331	j-invariant
L	1.7069125392019	L(r)(E,1)/r!
Ω	0.56897084640062	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	704f2 44a2 6336r2 17600o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704d2

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	2	-	4	6	-8	-3	0	5	1	0	10	0	6	-3	4	1	15	-4	2	-6	-9	-7

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Quadratic twists for elliptic curve 704d2

-4	8	-3	5	-7	-11	13
704f2	44a2	6336r2	17600o2	34496bj2	7744h2	118976i2

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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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