Elliptic curve isogeny class with LMFDB label 221952.d (Cremona label 221952bh)

• Label: 221952.d
• Number of curves: $4$
• Conductor: $221952$
• CM: no
• Rank: $1$

Elliptic curves in class 221952.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
221952.d1	221952bh3	$[0, -1, 0, -187079, -31082421]$	$58591911104/243$	$3003099784704$	$[2]$	$819200$	$1.6036$
221952.d2	221952bh4	$[0, -1, 0, -184189, -32092187]$	$-873722816/59049$	$-46704207851716608$	$[2]$	$1638400$	$1.9502$
221952.d3	221952bh1	$[0, -1, 0, -2119, 37099]$	$85184/3$	$37075305984$	$[2]$	$163840$	$0.79889$	$\Gamma_0(N)$-optimal
221952.d4	221952bh2	$[0, -1, 0, 771, 127845]$	$64/9$	$-7118458748928$	$[2]$	$327680$	$1.1455$

Rank

The elliptic curves in class 221952.d have rank $1$.

Complex multiplication

The elliptic curves in class 221952.d do not have complex multiplication.

Modular form 221952.2.a.d

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.

$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.