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	5382h	Isogeny class
Conductor	5382	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	2066688 = 28 · 33 · 13 · 23	Discriminant
Eigenvalues	2- 3+  0  0 -4 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-35,-29]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	170953875/76544	j-invariant
L	5.6153815264018	L(r)(E,1)/r!
Ω	2.0511507123371	Real period
R	0.68441844529354	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	43056x1 5382a1 69966a1 123786y1	Quadratic twists by: -4 -3 13 -23

Hecke Eigenvalues for elliptic curve 5382h1

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
-	+	0	0	-4	-	2	0	+	0	-10	-10	-10	6	8	6	4	-6	-8	0	14	-2	8	-8	-2

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Quadratic twists for elliptic curve 5382h1

-4	-3	13	-23
43056x1	5382a1	69966a1	123786y1

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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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