Cremona's table of elliptic curves

5382 = 2 · 3² · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 23-	Signs for the Atkin-Lehner involutions
Class	5382p	Isogeny class
Conductor	5382	Conductor
∏ cp	480	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	-2334677574048768 = -1 · 210 · 38 · 134 · 233	Discriminant
Eigenvalues	2- 3- -2 -2 -2 13-  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-46391,4505487]	[a1,a2,a3,a4,a6]
Generators	[-175:2778:1]	Generators of the group modulo torsion
j	-15145674183260713/3202575547392	j-invariant
L	4.8546962500997	L(r)(E,1)/r!
Ω	0.44032583126971	Real period
R	0.09187696748907	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	43056bn1 1794b1 69966q1 123786bl1	Quadratic twists by: -4 -3 13 -23

Hecke Eigenvalues for elliptic curve 5382p1

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	4	-	-6	8	-8	-2	4	-8	-2	-4	-8	8	8	-10	14	-6	-8	-2

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Quadratic twists for elliptic curve 5382p1

-4	-3	13	-23
43056bn1	1794b1	69966q1	123786bl1

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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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