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

• Label: 277200gs
• Number of curves: $2$
• Conductor: $277200$
• CM: no
• Rank: $1$

Elliptic curves in class 277200gs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277200.gs1	277200gs1	\([0, 0, 0, -105075, 13107250]\)	\(74246873427/16940\)	\(29272320000000\)	\([2]\)	\(1179648\)	\(1.5758\)	\(\Gamma_0(N)\)-optimal
277200.gs2	277200gs2	\([0, 0, 0, -93075, 16215250]\)	\(-51603494067/35870450\)	\(-61984137600000000\)	\([2]\)	\(2359296\)	\(1.9223\)

Rank

The elliptic curves in class 277200gs have rank \(1\).

Complex multiplication

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

Modular form 277200.2.a.gs

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.