Elliptic curve isogeny class with Cremona label 412090bn (LMFDB label 412090.bn)

• Label: 412090bn
• Number of curves: $2$
• Conductor: $412090$
• CM: no
• Rank: $1$

Elliptic curves in class 412090bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
412090.bn1	412090bn1	\([1, -1, 0, -110749, -14158327]\)	\(-5154200289/20\)	\(-582926854580\)	\([]\)	\(2751840\)	\(1.4708\)	\(\Gamma_0(N)\)-optimal^*
412090.bn2	412090bn2	\([1, -1, 0, 772301, 134406005]\)	\(1747829720511/1280000000\)	\(-37307318693120000000\)	\([]\)	\(19262880\)	\(2.4438\)	\(\Gamma_0(N)\)-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 412090bn1.

Rank

The elliptic curves in class 412090bn have rank \(1\).

Complex multiplication

The elliptic curves in class 412090bn do not have complex multiplication.

Modular form 412090.2.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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.