Elliptic curve isogeny class with Cremona label 11271f (LMFDB label 11271.g)

• Label: 11271f
• Number of curves: $4$
• Conductor: $11271$
• CM: no
• Rank: $1$

Elliptic curves in class 11271f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11271.g4	11271f1	\([1, 0, 1, 138, -1325]\)	\(12167/39\)	\(-941365191\)	\([2]\)	\(5120\)	\(0.40509\)	\(\Gamma_0(N)\)-optimal
11271.g3	11271f2	\([1, 0, 1, -1307, -15775]\)	\(10218313/1521\)	\(36713242449\)	\([2, 2]\)	\(10240\)	\(0.75167\)
11271.g1	11271f3	\([1, 0, 1, -20092, -1097791]\)	\(37159393753/1053\)	\(25416860157\)	\([2]\)	\(20480\)	\(1.0982\)
11271.g2	11271f4	\([1, 0, 1, -5642, 147221]\)	\(822656953/85683\)	\(2068179324627\)	\([2]\)	\(20480\)	\(1.0982\)

Rank

The elliptic curves in class 11271f have rank \(1\).

Complex multiplication

The elliptic curves in class 11271f do not have complex multiplication.

Modular form 11271.2.a.f

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.