Elliptic curve isogeny class with Cremona label 3120q (LMFDB label 3120.b)

• Label: 3120q
• Number of curves: $4$
• Conductor: $3120$
• CM: no
• Rank: $1$

Elliptic curves in class 3120q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3120.b3	3120q1	$[0, -1, 0, -96, -2304]$	$-24137569/561600$	$-2300313600$	$[2]$	$1152$	$0.47709$	$\Gamma_0(N)$-optimal
3120.b2	3120q2	$[0, -1, 0, -3296, -71424]$	$967068262369/4928040$	$20185251840$	$[2]$	$2304$	$0.82366$
3120.b4	3120q3	$[0, -1, 0, 864, 61440]$	$17394111071/411937500$	$-1687296000000$	$[2]$	$3456$	$1.0264$
3120.b1	3120q4	$[0, -1, 0, -19136, 973440]$	$189208196468929/10860320250$	$44483871744000$	$[2]$	$6912$	$1.3730$

Rank

The elliptic curves in class 3120q have rank $1$.

Complex multiplication

The elliptic curves in class 3120q do not have complex multiplication.

Modular form 3120.2.a.q

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.