Elliptic curve isogeny class with Cremona label 414736k (LMFDB label 414736.k)

• Label: 414736k
• Number of curves: $2$
• Conductor: $414736$
• CM: no
• Rank: $0$

Elliptic curves in class 414736k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
414736.k2	414736k1	\([0, 1, 0, -88969512, -323776412492]\)	\(-3183010111/8464\)	\(-207102327115760177446912\)	\([2]\)	\(45416448\)	\(3.3487\)	\(\Gamma_0(N)\)-optimal^*
414736.k1	414736k2	\([0, 1, 0, -1424419432, -20692592772300]\)	\(13062552753151/92\)	\(2251112251258262798336\)	\([2]\)	\(90832896\)	\(3.6953\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 414736k1.

Rank

The elliptic curves in class 414736k have rank \(0\).

Complex multiplication

The elliptic curves in class 414736k do not have complex multiplication.

Modular form 414736.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.