Elliptic curve isogeny class with LMFDB label 55233.g (Cremona label 55233g)

• Label: 55233.g
• Number of curves: $4$
• Conductor: $55233$
• CM: no
• Rank: $1$

Elliptic curves in class 55233.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55233.g1	55233g4	\([1, -1, 1, -294644, -61485650]\)	\(82483294977/17\)	\(583039603233\)	\([2]\)	\(221184\)	\(1.6449\)
55233.g2	55233g2	\([1, -1, 1, -18479, -950282]\)	\(20346417/289\)	\(9911673254961\)	\([2, 2]\)	\(110592\)	\(1.2983\)
55233.g3	55233g3	\([1, -1, 1, -2234, -2574782]\)	\(-35937/83521\)	\(-2864473570683729\)	\([2]\)	\(221184\)	\(1.6449\)
55233.g4	55233g1	\([1, -1, 1, -2234, 17920]\)	\(35937/17\)	\(583039603233\)	\([2]\)	\(55296\)	\(0.95174\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 55233.g have rank \(1\).

Complex multiplication

The elliptic curves in class 55233.g do not have complex multiplication.

Modular form 55233.2.a.g

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 LMFDB 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 LMFDB labels.