Elliptic curve isogeny class with Cremona label 120b (LMFDB label 120.a)

• Label: 120b
• Number of curves: $4$
• Conductor: $120$
• CM: no
• Rank: $0$

Elliptic curves in class 120b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
120.a4	120b1	$[0, 1, 0, 4, 0]$	$21296/15$	$-3840$	$[2]$	$8$	$-0.62374$	$\Gamma_0(N)$-optimal
120.a3	120b2	$[0, 1, 0, -16, -16]$	$470596/225$	$230400$	$[2, 2]$	$16$	$-0.27717$
120.a1	120b3	$[0, 1, 0, -216, -1296]$	$546718898/405$	$829440$	$[2]$	$32$	$0.069403$
120.a2	120b4	$[0, 1, 0, -136, 560]$	$136835858/1875$	$3840000$	$[2]$	$32$	$0.069403$

Rank

The elliptic curves in class 120b have rank $0$.

Complex multiplication

The elliptic curves in class 120b do not have complex multiplication.

Modular form 120.2.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 Cremona 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 Cremona labels.