Elliptic curve isogeny class with Cremona label 10608r (LMFDB label 10608.j)

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

Elliptic curves in class 10608r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10608.j2	10608r1	$[0, -1, 0, -3153, -67104]$	$216727177216000/2738853$	$43821648$	$[2]$	$5760$	$0.61257$	$\Gamma_0(N)$-optimal
10608.j3	10608r2	$[0, -1, 0, -3068, -70980]$	$-12479332642000/1526829993$	$-390868478208$	$[2]$	$11520$	$0.95915$
10608.j1	10608r3	$[0, -1, 0, -4953, 19764]$	$840033089536000/477272151837$	$7636354429392$	$[2]$	$17280$	$1.1619$
10608.j4	10608r4	$[0, -1, 0, 19612, 137676]$	$3258571509326000/1920843121977$	$-491735839226112$	$[2]$	$34560$	$1.5085$

Rank

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

Complex multiplication

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

Modular form 10608.2.a.r

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.