Elliptic curve isogeny class with Cremona label 10608z (LMFDB label 10608.q)

• Label: 10608z
• Number of curves: $4$
• Conductor: $10608$
• CM: no
• Rank: $1$

Elliptic curves in class 10608z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10608.q4	10608z1	$[0, 1, 0, 136, -1068]$	$67419143/169728$	$-695205888$	$[2]$	$3072$	$0.38045$	$\Gamma_0(N)$-optimal
10608.q3	10608z2	$[0, 1, 0, -1144, -12844]$	$40459583737/7033104$	$28807593984$	$[2, 2]$	$6144$	$0.72702$
10608.q1	10608z3	$[0, 1, 0, -17464, -894124]$	$143820170742457/5826444$	$23865114624$	$[2]$	$12288$	$1.0736$
10608.q2	10608z4	$[0, 1, 0, -5304, 135252]$	$4029546653497/351790452$	$1440933691392$	$[4]$	$12288$	$1.0736$

Rank

The elliptic curves in class 10608z have rank $1$.

Complex multiplication

The elliptic curves in class 10608z do not have complex multiplication.

Modular form 10608.2.a.z

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.