Elliptic curve isogeny class with LMFDB label 404544.fg (Cremona label 404544fg)

• Label: 404544.fg
• Number of curves: $2$
• Conductor: $404544$
• CM: no
• Rank: $1$

Elliptic curves in class 404544.fg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
404544.fg1	404544fg2	\([0, 1, 0, -187849601, 991031767263]\)	\(-23769846831649063249/3261823333284\)	\(-100597826410913285013504\)	\([]\)	\(85349376\)	\(3.4316\)	\(\Gamma_0(N)\)-optimal^*
404544.fg2	404544fg1	\([0, 1, 0, 498559, -302552097]\)	\(444369620591/1540767744\)	\(-47518786339171467264\)	\([]\)	\(12192768\)	\(2.4586\)	\(\Gamma_0(N)\)-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 404544.fg1.

Rank

The elliptic curves in class 404544.fg have rank \(1\).

Complex multiplication

The elliptic curves in class 404544.fg do not have complex multiplication.

Modular form 404544.2.a.fg

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.