Elliptic curve isogeny class with Cremona label 40560bg (LMFDB label 40560.h)

• Label: 40560bg
• Number of curves: $8$
• Conductor: $40560$
• CM: no
• Rank: $0$

Elliptic curves in class 40560bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40560.h6	40560bg1	$[0, -1, 0, -297496, -62354384]$	$147281603041/5265$	$104092259880960$	$[2]$	$258048$	$1.7787$	$\Gamma_0(N)$-optimal
40560.h5	40560bg2	$[0, -1, 0, -311016, -56362320]$	$168288035761/27720225$	$548045748273254400$	$[2, 2]$	$516096$	$2.1253$
40560.h7	40560bg3	$[0, -1, 0, 567784, -317893200]$	$1023887723039/2798036865$	$-55318894683397263360$	$[2]$	$1032192$	$2.4719$
40560.h4	40560bg4	$[0, -1, 0, -1406136, 588444336]$	$15551989015681/1445900625$	$28586336869808640000$	$[2, 2]$	$1032192$	$2.4719$
40560.h8	40560bg5	$[0, -1, 0, 1635864, 2783551536]$	$24487529386319/183539412225$	$-3628686077060464742400$	$[2]$	$2064384$	$2.8185$
40560.h2	40560bg6	$[0, -1, 0, -21970056, 39643441200]$	$59319456301170001/594140625$	$11746522382400000000$	$[2, 2]$	$2064384$	$2.8185$
40560.h3	40560bg7	$[0, -1, 0, -21442776, 41636137776]$	$-55150149867714721/5950927734375$	$-117653469375000000000000$	$[2]$	$4128768$	$3.1650$
40560.h1	40560bg8	$[0, -1, 0, -351520056, 2536841521200]$	$242970740812818720001/24375$	$481908610560000$	$[2]$	$4128768$	$3.1650$

Rank

The elliptic curves in class 40560bg have rank $0$.

Complex multiplication

The elliptic curves in class 40560bg do not have complex multiplication.

Modular form 40560.2.a.bg

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.