Cremona's table of elliptic curves

722 = 2 · 19²

Field	Data	Notes
Atkin-Lehner	2- 19+	Signs for the Atkin-Lehner involutions
Class	722d	Isogeny class
Conductor	722	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2280	Modular degree for the optimal curve
Δ	-2581501582232 = -1 · 23 · 199	Discriminant
Eigenvalues	2-  3  2 -3 -2 -3 -1 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-429,77485]	[a1,a2,a3,a4,a6]
j	-27/8	j-invariant
L	3.9605703012679	L(r)(E,1)/r!
Ω	0.66009505021132	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	5776k1 23104i1 6498f1 18050d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 722d1

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
-	3	2	-3	-2	-3	-1	+	5	-3	-6	6	12	-10	-8	-3	3	0	15	0	-11	-12	2	6	12

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Quadratic twists for elliptic curve 722d1

-4	8	-3	5	-7	-11	13	-19
5776k1	23104i1	6498f1	18050d1	35378m1	87362j1	122018c1	722b1

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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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