Cremona's table of elliptic curves

722 = 2 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 19+	Signs for the Atkin-Lehner involutions
Class	722a	Isogeny class
Conductor	722	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-8695584276992 = -1 · 29 · 198	Discriminant
Eigenvalues	2+  1  0 -4  3  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-33581,-2375576]	[a1,a2,a3,a4,a6]
Generators	[1474:55398:1]	Generators of the group modulo torsion
j	-246579625/512	j-invariant
L	1.81917063743	L(r)(E,1)/r!
Ω	0.17631678843805	Real period
R	3.4392085850051	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	5776i2 23104c2 6498s2 18050p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 722a2

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	0	-4	3	2	-6	+	-6	0	2	-10	9	-4	0	6	-9	-4	-7	-6	-1	-4	3	6	17

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Quadratic twists for elliptic curve 722a2

-4	8	-3	5	-7	-11	13	-19
5776i2	23104c2	6498s2	18050p2	35378c2	87362x2	122018v2	722f2

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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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