Elliptic curve isogeny class with LMFDB label 457776.fg (Cremona label 457776fg)

• Label: 457776.fg
• Number of curves: $4$
• Conductor: $457776$
• CM: no
• Rank: $1$

Elliptic curves in class 457776.fg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
457776.fg1	457776fg3	\([0, 0, 0, -20139627099, 1100058556561418]\)	\(12534210458299016895673/315581882565708\)	\(22745373206149456942399930368\)	\([2]\)	\(849346560\)	\(4.5493\)	\(\Gamma_0(N)\)-optimal^*
457776.fg2	457776fg2	\([0, 0, 0, -1306722459, 15806804046410]\)	\(3423676911662954233/483711578981136\)	\(34863219328729953918656249856\)	\([2, 2]\)	\(424673280\)	\(4.2028\)	\(\Gamma_0(N)\)-optimal^*
457776.fg3	457776fg1	\([0, 0, 0, -344560539, -2215066012342]\)	\(62768149033310713/6915442583808\)	\(498426339229600278635347968\)	\([2]\)	\(212336640\)	\(3.8562\)	\(\Gamma_0(N)\)-optimal^*
457776.fg4	457776fg4	\([0, 0, 0, 2131591461, 84954735291530]\)	\(14861225463775641287/51859390496937804\)	\(-3737734186469629986328285200384\)	\([2]\)	\(849346560\)	\(4.5493\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 457776.fg1.

Rank

The elliptic curves in class 457776.fg have rank \(1\).

Complex multiplication

The elliptic curves in class 457776.fg do not have complex multiplication.

Modular form 457776.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.