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
deg	720	Modular degree for the optimal curve
Δ	-28603895648 = -1 · 25 · 197	Discriminant
Eigenvalues	2+  1 -4  3  2  1  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8,-8138]	[a1,a2,a3,a4,a6]
j	-1/608	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	5776o1 23104r1 6498x1 18050u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 722c1

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 722c1

-4	8	-3	5	-7	-11	13	-19
5776o1	23104r1	6498x1	18050u1	35378g1	87362bm1	122018bf1	38b1

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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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