Elliptic curve isogeny class with LMFDB label 5712.b (Cremona label 5712n)

• Label: 5712.b
• Number of curves: $2$
• Conductor: $5712$
• CM: no
• Rank: $1$

Elliptic curves in class 5712.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5712.b1	5712n1	$[0, -1, 0, -2997, -63639]$	$-11632923639808/318495051$	$-81534733056$	$[]$	$6912$	$0.87493$	$\Gamma_0(N)$-optimal
5712.b2	5712n2	$[0, -1, 0, 13323, -265191]$	$1021544365555712/705905647251$	$-180711845696256$	$[]$	$20736$	$1.4242$

Rank

The elliptic curves in class 5712.b have rank $1$.

Complex multiplication

The elliptic curves in class 5712.b do not have complex multiplication.

Modular form 5712.2.a.b

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.