Cremona's table of elliptic curves

5478 = 2 · 3 · 11 · 83

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 83-	Signs for the Atkin-Lehner involutions
Class	5478i	Isogeny class
Conductor	5478	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	10002828 = 22 · 3 · 112 · 832	Discriminant
Eigenvalues	2- 3+  0  2 11+ -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-83,-283]	[a1,a2,a3,a4,a6]
Generators	[-5:8:1]	Generators of the group modulo torsion
j	63282696625/10002828	j-invariant
L	5.1300356125347	L(r)(E,1)/r!
Ω	1.5984884739802	Real period
R	1.6046520497458	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	43824bh2 16434g2 60258d2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 5478i2

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

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Quadratic twists for elliptic curve 5478i2

-4	-3	-11
43824bh2	16434g2	60258d2

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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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