Elliptic curve isogeny class with Cremona label 1850f (LMFDB label 1850.e)

• Label: 1850f
• Number of curves: $2$
• Conductor: $1850$
• CM: no
• Rank: $1$

Elliptic curves in class 1850f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1850.e2	1850f1	$[1, -1, 0, -857, -9299]$	$557238592989/9699328$	$1212416000$	$[2]$	$864$	$0.53975$	$\Gamma_0(N)$-optimal
1850.e1	1850f2	$[1, -1, 0, -13657, -610899]$	$2253707317528029/700928$	$87616000$	$[2]$	$1728$	$0.88632$

Rank

The elliptic curves in class 1850f have rank $1$.

Complex multiplication

The elliptic curves in class 1850f do not have complex multiplication.

Modular form 1850.2.a.f

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.