Cremona's table of elliptic curves

722 = 2 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 19-	Signs for the Atkin-Lehner involutions
Class	722c	Isogeny class
Conductor	722	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-232980517796438 = -1 · 2 · 1911	Discriminant
Eigenvalues	2+  1 -4  3  2  1  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-25278,1710222]	[a1,a2,a3,a4,a6]
j	-37966934881/4952198	j-invariant
L	1.0809896957436	L(r)(E,1)/r!
Ω	0.54049484787181	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	5776o2 23104r2 6498x2 18050u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 722c2

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

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Quadratic twists for elliptic curve 722c2

-4	8	-3	5	-7	-11	13	-19
5776o2	23104r2	6498x2	18050u2	35378g2	87362bm2	122018bf2	38b2

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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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