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	19360m	Isogeny class
Conductor	19360	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	115200	Modular degree for the optimal curve
Δ	42871776200000 = 26 · 55 · 118	Discriminant
Eigenvalues	2+ -2 5-  0 11- -4  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-504610,-138137100]	[a1,a2,a3,a4,a6]
Generators	[-410:10:1]	Generators of the group modulo torsion
j	125330290485184/378125	j-invariant
L	3.5150280514644	L(r)(E,1)/r!
Ω	0.17912681271595	Real period
R	1.9623126198523	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19360l1 38720cf2 96800bv1 1760l1	Quadratic twists by: -4 8 5 -11

Hecke Eigenvalues for elliptic curve 19360m1

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
+	-2	-	0	-	-4	4	4	-2	-6	-4	2	2	4	2	2	4	2	-10	-8	-4	16	-4	-10	-18

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Quadratic twists for elliptic curve 19360m1

-4	8	5	-11
19360l1	38720cf2	96800bv1	1760l1

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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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