Cremona's table of elliptic curves

26928 = 2⁴ · 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 17+	Signs for the Atkin-Lehner involutions
Class	26928bd	Isogeny class
Conductor	26928	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	113909317632 = 214 · 37 · 11 · 172	Discriminant
Eigenvalues	2- 3- -2  2 11+  4 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1731,22466]	[a1,a2,a3,a4,a6]
Generators	[1:144:1]	Generators of the group modulo torsion
j	192100033/38148	j-invariant
L	5.1217638144013	L(r)(E,1)/r!
Ω	0.99767019473239	Real period
R	0.64171554906668	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	3366i1 107712ek1 8976v1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 26928bd1

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

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Quadratic twists for elliptic curve 26928bd1

-4	8	-3
3366i1	107712ek1	8976v1

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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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