Cremona's table of elliptic curves

26832 = 2⁴ · 3 · 13 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 43-	Signs for the Atkin-Lehner involutions
Class	26832r	Isogeny class
Conductor	26832	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7168	Modular degree for the optimal curve
Δ	89296896 = 212 · 3 · 132 · 43	Discriminant
Eigenvalues	2- 3-  2 -2  2 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-112,20]	[a1,a2,a3,a4,a6]
j	38272753/21801	j-invariant
L	3.2787017700072	L(r)(E,1)/r!
Ω	1.6393508850036	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1677a1 107328bu1 80496bh1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 26832r1

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	+	-6	2	4	6	0	0	12	-	6	6	6	-10	4	16	4	-16	14	-10	14

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Quadratic twists for elliptic curve 26832r1

-4	8	-3
1677a1	107328bu1	80496bh1

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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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