Elliptic curve isogeny class with LMFDB label 82110.bp (Cremona label 82110bq)

• Label: 82110.bp
• Number of curves: $4$
• Conductor: $82110$
• CM: no
• Rank: $0$

Elliptic curves in class 82110.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82110.bp1	82110bq4	$[1, 0, 0, -180201, 17385795]$	$647135840104522706449/243695383641033030$	$243695383641033030$	$[2]$	$1376256$	$2.0358$
82110.bp2	82110bq2	$[1, 0, 0, -79051, -8366995]$	$54631881784005100849/1420422278480100$	$1420422278480100$	$[2, 2]$	$688128$	$1.6893$
82110.bp3	82110bq1	$[1, 0, 0, -78551, -8480295]$	$53601780056497828849/37688490000$	$37688490000$	$[2]$	$344064$	$1.3427$	$\Gamma_0(N)$-optimal
82110.bp4	82110bq3	$[1, 0, 0, 14099, -26866585]$	$309946487145592751/312030025063117830$	$-312030025063117830$	$[2]$	$1376256$	$2.0358$

Rank

The elliptic curves in class 82110.bp have rank $0$.

Complex multiplication

The elliptic curves in class 82110.bp do not have complex multiplication.

Modular form 82110.2.a.bp

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.

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.