Cremona's table of elliptic curves

19680 = 2⁵ · 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 41-	Signs for the Atkin-Lehner involutions
Class	19680p	Isogeny class
Conductor	19680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2286981941760 = 29 · 312 · 5 · 412	Discriminant
Eigenvalues	2- 3+ 5+ -2 -2  2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10016,382260]	[a1,a2,a3,a4,a6]
Generators	[49:82:1]	Generators of the group modulo torsion
j	217060129661192/4466761605	j-invariant
L	3.3413309969727	L(r)(E,1)/r!
Ω	0.81947063292973	Real period
R	2.0387130805572	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	19680y2 39360dd2 59040u2 98400ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 19680p2

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	-2	2	-4	2	4	0	0	6	-	-4	-6	6	0	-14	-4	0	-6	4	-4	14	12

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Quadratic twists for elliptic curve 19680p2

-4	8	-3	5
19680y2	39360dd2	59040u2	98400ba2

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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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