Elliptic curve isogeny class with LMFDB label 447700.g (Cremona label 447700g)

• Label: 447700.g
• Number of curves: $2$
• Conductor: $447700$
• CM: no
• Rank: $1$

Elliptic curves in class 447700.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
447700.g1	447700g2	$[0, -1, 0, -36364533, 84416475937]$	$750484394082304/578125$	$4096734812500000000$	$[]$	$13996800$	$2.8793$	$\Gamma_0(N)$-optimal^*
447700.g2	447700g1	$[0, -1, 0, -548533, 60841937]$	$2575826944/1266325$	$8973487933300000000$	$[]$	$4665600$	$2.3299$	$\Gamma_0(N)$-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 447700.g1.

Rank

The elliptic curves in class 447700.g have rank $1$.

Complex multiplication

The elliptic curves in class 447700.g do not have complex multiplication.

Modular form 447700.2.a.g

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.