Elliptic curve isogeny class with Cremona label 3600bf (LMFDB label 3600.u)

• Label: 3600bf
• Number of curves: $8$
• Conductor: $3600$
• CM: no
• Rank: $1$

Elliptic curves in class 3600bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3600.u7	3600bf1	$[0, 0, 0, -75, 40250]$	$-1/15$	$-699840000000$	$[2]$	$3072$	$0.95175$	$\Gamma_0(N)$-optimal
3600.u6	3600bf2	$[0, 0, 0, -18075, 922250]$	$13997521/225$	$10497600000000$	$[2, 2]$	$6144$	$1.2983$
3600.u5	3600bf3	$[0, 0, 0, -36075, -1219750]$	$111284641/50625$	$2361960000000000$	$[2, 2]$	$12288$	$1.6449$
3600.u4	3600bf4	$[0, 0, 0, -288075, 59512250]$	$56667352321/15$	$699840000000$	$[4]$	$12288$	$1.6449$
3600.u2	3600bf5	$[0, 0, 0, -486075, -130369750]$	$272223782641/164025$	$7652750400000000$	$[2, 2]$	$24576$	$1.9915$
3600.u8	3600bf6	$[0, 0, 0, 125925, -9157750]$	$4733169839/3515625$	$-164025000000000000$	$[2]$	$24576$	$1.9915$
3600.u1	3600bf7	$[0, 0, 0, -7776075, -8346199750]$	$1114544804970241/405$	$18895680000000$	$[2]$	$49152$	$2.3380$
3600.u3	3600bf8	$[0, 0, 0, -396075, -180139750]$	$-147281603041/215233605$	$-10041939074880000000$	$[2]$	$49152$	$2.3380$

Rank

The elliptic curves in class 3600bf have rank $1$.

Complex multiplication

The elliptic curves in class 3600bf do not have complex multiplication.

Modular form 3600.2.a.bf

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.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.