Elliptic curve isogeny class with Cremona label 409101bt (LMFDB label 409101.bt)

• Label: 409101bt
• Number of curves: $2$
• Conductor: $409101$
• CM: no
• Rank: $1$

Elliptic curves in class 409101bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
409101.bt2	409101bt1	\([1, 0, 1, -136491, -282253919]\)	\(-1349232625/164333367\)	\(-34250751478179129663\)	\([2]\)	\(6912000\)	\(2.4278\)	\(\Gamma_0(N)\)-optimal^*
409101.bt1	409101bt2	\([1, 0, 1, -7340226, -7595485691]\)	\(209849322390625/1882056627\)	\(392262721661615299803\)	\([2]\)	\(13824000\)	\(2.7744\)	\(\Gamma_0(N)\)-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 409101bt1.

Rank

The elliptic curves in class 409101bt have rank \(1\).

Complex multiplication

The elliptic curves in class 409101bt do not have complex multiplication.

Modular form 409101.2.a.bt

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.