Elliptic curve isogeny class with LMFDB label 4800.cq (Cremona label 4800w)

• Label: 4800.cq
• Number of curves: $8$
• Conductor: $4800$
• CM: no
• Rank: $0$

Elliptic curves in class 4800.cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4800.cq1	4800w7	$[0, 1, 0, -8533633, -9597935137]$	$16778985534208729/81000$	$331776000000000$	$[2]$	$110592$	$2.4086$
4800.cq2	4800w8	$[0, 1, 0, -725633, -32623137]$	$10316097499609/5859375000$	$24000000000000000000$	$[2]$	$110592$	$2.4086$
4800.cq3	4800w6	$[0, 1, 0, -533633, -149935137]$	$4102915888729/9000000$	$36864000000000000$	$[2, 2]$	$55296$	$2.0620$
4800.cq4	4800w5	$[0, 1, 0, -461633, 120568863]$	$2656166199049/33750$	$138240000000000$	$[2]$	$36864$	$1.8593$
4800.cq5	4800w4	$[0, 1, 0, -109633, -12071137]$	$35578826569/5314410$	$21767823360000000$	$[2]$	$36864$	$1.8593$
4800.cq6	4800w2	$[0, 1, 0, -29633, 1768863]$	$702595369/72900$	$298598400000000$	$[2, 2]$	$18432$	$1.5127$
4800.cq7	4800w3	$[0, 1, 0, -21633, -4015137]$	$-273359449/1536000$	$-6291456000000000$	$[2]$	$27648$	$1.7155$
4800.cq8	4800w1	$[0, 1, 0, 2367, 136863]$	$357911/2160$	$-8847360000000$	$[2]$	$9216$	$1.1662$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 4800.cq have rank $0$.

Complex multiplication

The elliptic curves in class 4800.cq do not have complex multiplication.

Modular form 4800.2.a.cq

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.

$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.