Elliptic curve isogeny class with Cremona label 2880bb (LMFDB label 2880.q)

• Label: 2880bb
• Number of curves: $8$
• Conductor: $2880$
• CM: no
• Rank: $1$

Elliptic curves in class 2880bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2880.q8	2880bb1	$[0, 0, 0, 852, 29392]$	$357911/2160$	$-412782428160$	$[2]$	$3072$	$0.91074$	$\Gamma_0(N)$-optimal
2880.q6	2880bb2	$[0, 0, 0, -10668, 384208]$	$702595369/72900$	$13931406950400$	$[2, 2]$	$6144$	$1.2573$
2880.q7	2880bb3	$[0, 0, 0, -7788, -865712]$	$-273359449/1536000$	$-293534171136000$	$[2]$	$9216$	$1.4600$
2880.q5	2880bb4	$[0, 0, 0, -39468, -2599472]$	$35578826569/5314410$	$1015599566684160$	$[2]$	$12288$	$1.6039$
2880.q4	2880bb5	$[0, 0, 0, -166188, 26076112]$	$2656166199049/33750$	$6449725440000$	$[2]$	$12288$	$1.6039$
2880.q3	2880bb6	$[0, 0, 0, -192108, -32347568]$	$4102915888729/9000000$	$1719926784000000$	$[2, 2]$	$18432$	$1.8066$
2880.q1	2880bb7	$[0, 0, 0, -3072108, -2072539568]$	$16778985534208729/81000$	$15479341056000$	$[2]$	$36864$	$2.1532$
2880.q2	2880bb8	$[0, 0, 0, -261228, -6994352]$	$10316097499609/5859375000$	$1119744000000000000$	$[2]$	$36864$	$2.1532$

Rank

The elliptic curves in class 2880bb have rank $1$.

Complex multiplication

The elliptic curves in class 2880bb do not have complex multiplication.

Modular form 2880.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.