Cremona's table of elliptic curves

722 = 2 · 19²

Field	Data	Notes
Atkin-Lehner	2- 19-	Signs for the Atkin-Lehner involutions
Class	722f	Isogeny class
Conductor	722	Conductor
∏ cp	9	Product of Tamagawa factors cp
Δ	-184832 = -1 · 29 · 192	Discriminant
Eigenvalues	2- -1  0 -4  3 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-93,307]	[a1,a2,a3,a4,a6]
Generators	[7:-12:1]	Generators of the group modulo torsion
j	-246579625/512	j-invariant
L	2.5300549409878	L(r)(E,1)/r!
Ω	3.2014095798617	Real period
R	0.087810449944821	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	5776m2 23104n2 6498l2 18050g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 722f2

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 722f2

-4	8	-3	5	-7	-11	13	-19
5776m2	23104n2	6498l2	18050g2	35378n2	87362r2	122018k2	722a2

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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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