Elliptic curve isogeny class with Cremona label 56784cb (LMFDB label 56784.h)

• Label: 56784cb
• Number of curves: $4$
• Conductor: $56784$
• CM: no
• Rank: $1$

Elliptic curves in class 56784cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
56784.h3	56784cb1	$[0, -1, 0, -18984, 908400]$	$38272753/4368$	$86358023012352$	$[2]$	$193536$	$1.4064$	$\Gamma_0(N)$-optimal
56784.h2	56784cb2	$[0, -1, 0, -73064, -6619536]$	$2181825073/298116$	$5893935070593024$	$[2, 2]$	$387072$	$1.7530$
56784.h4	56784cb3	$[0, -1, 0, 116216, -35390096]$	$8780064047/32388174$	$-640333945883713536$	$[2]$	$774144$	$2.0996$
56784.h1	56784cb4	$[0, -1, 0, -1127624, -460502160]$	$8020417344913/187278$	$3702600236654592$	$[2]$	$774144$	$2.0996$

Rank

The elliptic curves in class 56784cb have rank $1$.

Complex multiplication

The elliptic curves in class 56784cb do not have complex multiplication.

Modular form 56784.2.a.cb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.