Elliptic curve isogeny class with Cremona label 1911f (LMFDB label 1911.f)

• Label: 1911f
• Number of curves: $4$
• Conductor: $1911$
• CM: no
• Rank: $1$

Elliptic curves in class 1911f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1911.f4	1911f1	\([1, 0, 1, 23, 95]\)	\(12167/39\)	\(-4588311\)	\([2]\)	\(288\)	\(-0.038559\)	\(\Gamma_0(N)\)-optimal
1911.f3	1911f2	\([1, 0, 1, -222, 1075]\)	\(10218313/1521\)	\(178944129\)	\([2, 2]\)	\(576\)	\(0.30801\)
1911.f2	1911f3	\([1, 0, 1, -957, -10391]\)	\(822656953/85683\)	\(10080519267\)	\([2]\)	\(1152\)	\(0.65459\)
1911.f1	1911f4	\([1, 0, 1, -3407, 76241]\)	\(37159393753/1053\)	\(123884397\)	\([2]\)	\(1152\)	\(0.65459\)

Rank

The elliptic curves in class 1911f have rank \(1\).

Complex multiplication

The elliptic curves in class 1911f do not have complex multiplication.

Modular form 1911.2.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.