Elliptic curve isogeny class with LMFDB label 436425.bn (Cremona label 436425bn)

• Label: 436425.bn
• Number of curves: $2$
• Conductor: $436425$
• CM: no
• Rank: $1$

Elliptic curves in class 436425.bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
436425.bn1	436425bn1	\([0, 1, 1, -308583, -69316756]\)	\(-56197120/3267\)	\(-188919238032421875\)	\([]\)	\(4276800\)	\(2.0713\)	\(\Gamma_0(N)\)-optimal^*
436425.bn2	436425bn2	\([0, 1, 1, 1675167, -121886131]\)	\(8990228480/5314683\)	\(-307329618225854296875\)	\([]\)	\(12830400\)	\(2.6206\)	\(\Gamma_0(N)\)-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 436425.bn1.

Rank

The elliptic curves in class 436425.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 436425.bn do not have complex multiplication.

Modular form 436425.2.a.bn

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.