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	19360b	Isogeny class
Conductor	19360	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-3407360 = -1 · 29 · 5 · 113	Discriminant
Eigenvalues	2+ -1 5+  1 11+  0  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-216,1300]	[a1,a2,a3,a4,a6]
Generators	[4:22:1]	Generators of the group modulo torsion
j	-1643032/5	j-invariant
L	3.6949281730052	L(r)(E,1)/r!
Ω	2.5166921867766	Real period
R	0.36704212303151	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	19360a1 38720cp1 96800bj1 19360o1	Quadratic twists by: -4 8 5 -11

Hecke Eigenvalues for elliptic curve 19360b1

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	+	0	3	-5	4	3	-7	-1	-6	8	6	-1	0	5	-4	-9	2	-16	4	1	10

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Quadratic twists for elliptic curve 19360b1

-4	8	5	-11
19360a1	38720cp1	96800bj1	19360o1

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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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