Elliptic curve isogeny class with Cremona label 34656x (LMFDB label 34656.i)

• Label: 34656x
• Number of curves: $4$
• Conductor: $34656$
• CM: no
• Rank: $1$

Elliptic curves in class 34656x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
34656.i3	34656x1	\([0, -1, 0, -842, -4800]\)	\(21952/9\)	\(27098427456\)	\([2, 2]\)	\(27648\)	\(0.69943\)	\(\Gamma_0(N)\)-optimal
34656.i4	34656x2	\([0, -1, 0, 2768, -38012]\)	\(97336/81\)	\(-1951086776832\)	\([2]\)	\(55296\)	\(1.0460\)
34656.i2	34656x3	\([0, -1, 0, -6257, 189057]\)	\(140608/3\)	\(578099785728\)	\([2]\)	\(55296\)	\(1.0460\)
34656.i1	34656x4	\([0, -1, 0, -11672, -481320]\)	\(7301384/3\)	\(72262473216\)	\([2]\)	\(55296\)	\(1.0460\)

Rank

The elliptic curves in class 34656x have rank \(1\).

Complex multiplication

The elliptic curves in class 34656x do not have complex multiplication.

Modular form 34656.2.a.x

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.