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	5382f	Isogeny class
Conductor	5382	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	76819170189622068 = 22 · 310 · 133 · 236	Discriminant
Eigenvalues	2+ 3-  0  2 -6 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-401292,97032492]	[a1,a2,a3,a4,a6]
j	9803435555023890625/105376090795092	j-invariant
L	1.3814768898241	L(r)(E,1)/r!
Ω	0.34536922245602	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	43056bl4 1794i4 69966bd4 123786t4	Quadratic twists by: -4 -3 13 -23

Hecke Eigenvalues for elliptic curve 5382f4

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	2	-6	-	6	2	-	6	8	-4	-6	-4	0	6	0	2	14	-12	-10	8	6	0	8

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Quadratic twists for elliptic curve 5382f4

-4	-3	13	-23
43056bl4	1794i4	69966bd4	123786t4

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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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