Elliptic curve isogeny class with LMFDB label 80.b (Cremona label 80b)

• Label: 80.b
• Number of curves: $4$
• Conductor: $80$
• CM: no
• Rank: $0$

Elliptic curves in class 80.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
80.b1	80b4	$[0, -1, 0, -41, 116]$	$488095744/125$	$2000$	$[2]$	$24$	$-0.38064$
80.b2	80b3	$[0, -1, 0, -36, 140]$	$-20720464/15625$	$-4000000$	$[2]$	$12$	$-0.034070$
80.b3	80b2	$[0, -1, 0, -1, 0]$	$16384/5$	$80$	$[2]$	$8$	$-0.92995$
80.b4	80b1	$[0, -1, 0, 4, -4]$	$21296/25$	$-6400$	$[2]$	$4$	$-0.58338$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 80.b have rank $0$.

Complex multiplication

The elliptic curves in class 80.b do not have complex multiplication.

Modular form 80.2.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.

$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.