Elliptic curve isogeny class with Cremona label 23534e (LMFDB label 23534.o)

• Label: 23534e
• Number of curves: $6$
• Conductor: $23534$
• CM: no
• Rank: $1$

Elliptic curves in class 23534e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23534.o5	23534e1	$[1, 1, 0, -875, 19817]$	$-15625/28$	$-133002918748$	$[2]$	$23040$	$0.82470$	$\Gamma_0(N)$-optimal
23534.o4	23534e2	$[1, 1, 0, -17685, 897299]$	$128787625/98$	$465510215618$	$[2]$	$46080$	$1.1713$
23534.o6	23534e3	$[1, 1, 0, 7530, -418924]$	$9938375/21952$	$-104274288298432$	$[2]$	$69120$	$1.3740$
23534.o3	23534e4	$[1, 1, 0, -59710, -4628148]$	$4956477625/941192$	$4470760110795272$	$[2]$	$138240$	$1.7206$
23534.o2	23534e5	$[1, 1, 0, -286645, -59359827]$	$-548347731625/1835008$	$-8716479283068928$	$[2]$	$207360$	$1.9233$
23534.o1	23534e6	$[1, 1, 0, -4590005, -3786930259]$	$2251439055699625/25088$	$119170615198208$	$[2]$	$414720$	$2.2699$

Rank

The elliptic curves in class 23534e have rank $1$.

Complex multiplication

The elliptic curves in class 23534e do not have complex multiplication.

Modular form 23534.2.a.e

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.