Cremona's table of elliptic curves

38720 = 2⁶ · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2- 5- 11+	Signs for the Atkin-Lehner involutions
Class	38720cz	Isogeny class
Conductor	38720	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-3489136640 = -1 · 219 · 5 · 113	Discriminant
Eigenvalues	2- -3 5-  5 11+ -4 -1  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,308,1936]	[a1,a2,a3,a4,a6]
Generators	[0:44:1]	Generators of the group modulo torsion
j	9261/10	j-invariant
L	4.4013398698548	L(r)(E,1)/r!
Ω	0.93325273298942	Real period
R	1.1790321405649	Regulator
r	1	Rank of the group of rational points
S	0.99999999999923	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38720be1 9680n1 38720da1	Quadratic twists by: -4 8 -11

Hecke Eigenvalues for elliptic curve 38720cz1

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
-	-3	-	5	+	-4	-1	5	-4	5	1	-3	-2	-8	-6	-11	0	-5	-4	15	-6	8	-8	1	10

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Quadratic twists for elliptic curve 38720cz1

-4	8	-11
38720be1	9680n1	38720da1

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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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