Cremona's table of elliptic curves

19152 = 2⁴ · 3² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	19152r	Isogeny class
Conductor	19152	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	267396546816 = 28 · 310 · 72 · 192	Discriminant
Eigenvalues	2+ 3-  2 7+ -4  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1839,17390]	[a1,a2,a3,a4,a6]
Generators	[-38:180:1]	Generators of the group modulo torsion
j	3685542352/1432809	j-invariant
L	5.4879300724465	L(r)(E,1)/r!
Ω	0.89248250930184	Real period
R	3.0745308816974	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	9576z2 76608dz2 6384c2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 19152r2

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	+	-4	2	-2	-	0	2	8	-2	2	-4	0	2	-12	14	-8	-12	-14	4	-4	18	-10

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Quadratic twists for elliptic curve 19152r2

-4	8	-3
9576z2	76608dz2	6384c2

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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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