Elliptic curve isogeny class with Cremona label 61200fh (LMFDB label 61200.do)

• Label: 61200fh
• Number of curves: $6$
• Conductor: $61200$
• CM: no
• Rank: $0$

Elliptic curves in class 61200fh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61200.do5	61200fh1	$[0, 0, 0, -122475, 15300250]$	$4354703137/352512$	$16446799872000000$	$[2]$	$393216$	$1.8545$	$\Gamma_0(N)$-optimal
61200.do4	61200fh2	$[0, 0, 0, -410475, -83483750]$	$163936758817/30338064$	$1415452713984000000$	$[2, 2]$	$786432$	$2.2011$
61200.do6	61200fh3	$[0, 0, 0, 813525, -486179750]$	$1276229915423/2927177028$	$-136570371418368000000$	$[2]$	$1572864$	$2.5477$
61200.do2	61200fh4	$[0, 0, 0, -6242475, -6002963750]$	$576615941610337/27060804$	$1262548871424000000$	$[2, 2]$	$1572864$	$2.5477$
61200.do3	61200fh5	$[0, 0, 0, -5918475, -6653879750]$	$-491411892194497/125563633938$	$-5858296905011328000000$	$[2]$	$3145728$	$2.8942$
61200.do1	61200fh6	$[0, 0, 0, -99878475, -384198767750]$	$2361739090258884097/5202$	$242704512000000$	$[2]$	$3145728$	$2.8942$

Rank

The elliptic curves in class 61200fh have rank $0$.

Complex multiplication

The elliptic curves in class 61200fh do not have complex multiplication.

Modular form 61200.2.a.fh

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.