Elliptic curve isogeny class with Cremona label 33462k (LMFDB label 33462.u)

• Label: 33462k
• Number of curves: $4$
• Conductor: $33462$
• CM: no
• Rank: $2$

Elliptic curves in class 33462k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33462.u4	33462k1	\([1, -1, 0, -10932, 426960]\)	\(1108717875/45056\)	\(5871871070208\)	\([2]\)	\(73728\)	\(1.2160\)	\(\Gamma_0(N)\)-optimal
33462.u2	33462k2	\([1, -1, 0, -173172, 27780624]\)	\(4406910829875/7744\)	\(1009227840192\)	\([2]\)	\(147456\)	\(1.5625\)
33462.u3	33462k3	\([1, -1, 0, -132612, -18428032]\)	\(2714704875/21296\)	\(2023249512624912\)	\([2]\)	\(221184\)	\(1.7653\)
33462.u1	33462k4	\([1, -1, 0, -223872, 10245860]\)	\(13060888875/7086244\)	\(673236275325939468\)	\([2]\)	\(442368\)	\(2.1118\)

Rank

The elliptic curves in class 33462k have rank \(2\).

Complex multiplication

The elliptic curves in class 33462k do not have complex multiplication.

Modular form 33462.2.a.k

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.