Elliptic curve isogeny class with LMFDB label 344850.gz (Cremona label 344850gz)

• Label: 344850.gz
• Number of curves: $4$
• Conductor: $344850$
• CM: no
• Rank: $1$

Elliptic curves in class 344850.gz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
344850.gz1	344850gz3	\([1, 0, 0, -1878588, 989452542]\)	\(26487576322129/44531250\)	\(1232653527832031250\)	\([2]\)	\(7864320\)	\(2.3666\)
344850.gz2	344850gz2	\([1, 0, 0, -154338, 4905792]\)	\(14688124849/8122500\)	\(224836003476562500\)	\([2, 2]\)	\(3932160\)	\(2.0200\)
344850.gz3	344850gz1	\([1, 0, 0, -93838, -11005708]\)	\(3301293169/22800\)	\(631118606250000\)	\([2]\)	\(1966080\)	\(1.6734\)	\(\Gamma_0(N)\)-optimal
344850.gz4	344850gz4	\([1, 0, 0, 601912, 38937042]\)	\(871257511151/527800050\)	\(-14609843505907031250\)	\([2]\)	\(7864320\)	\(2.3666\)

Rank

The elliptic curves in class 344850.gz have rank \(1\).

Complex multiplication

The elliptic curves in class 344850.gz do not have complex multiplication.

Modular form 344850.2.a.gz

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.