Elliptic curve isogeny class with LMFDB label 277200.x (Cremona label 277200x)

• Label: 277200.x
• Number of curves: $4$
• Conductor: $277200$
• CM: no
• Rank: $1$

Elliptic curves in class 277200.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277200.x1	277200x3	$[0, 0, 0, -958005075, 11413000287250]$	$2084105208962185000201/31185000$	$1454967360000000000$	$[2]$	$56623104$	$3.4887$
277200.x2	277200x4	$[0, 0, 0, -64917075, 146529855250]$	$648474704552553481/176469171805080$	$8233345679737812480000000$	$[2]$	$56623104$	$3.4887$
277200.x3	277200x2	$[0, 0, 0, -59877075, 178317135250]$	$508859562767519881/62240270400$	$2903882055782400000000$	$[2, 2]$	$28311552$	$3.1421$
277200.x4	277200x1	$[0, 0, 0, -3429075, 3271887250]$	$-95575628340361/43812679680$	$-2044124383150080000000$	$[2]$	$14155776$	$2.7956$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 277200.x have rank $1$.

Complex multiplication

The elliptic curves in class 277200.x do not have complex multiplication.

Modular form 277200.2.a.x

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.