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.