Cremona's table of elliptic curves

19360 = 2⁵ · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	19360j	Isogeny class
Conductor	19360	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	50688	Modular degree for the optimal curve
Δ	-109751747072000 = -1 · 212 · 53 · 118	Discriminant
Eigenvalues	2+ -1 5-  1 11-  4  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1775,502625]	[a1,a2,a3,a4,a6]
Generators	[-40:605:1]	Generators of the group modulo torsion
j	704/125	j-invariant
L	4.7605150266447	L(r)(E,1)/r!
Ω	0.45800308283807	Real period
R	0.57744820274348	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	19360x1 38720h1 96800bn1 19360z1	Quadratic twists by: -4 8 5 -11

Hecke Eigenvalues for elliptic curve 19360j1

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	-	1	-	4	4	0	-8	10	-10	0	-3	9	-9	-12	6	3	1	-10	-4	2	-4	1	16

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Quadratic twists for elliptic curve 19360j1

-4	8	5	-11
19360x1	38720h1	96800bn1	19360z1

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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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