Elliptic curve isogeny class with LMFDB label 312325.o (Cremona label 312325o)

• Label: 312325.o
• Number of curves: $2$
• Conductor: $312325$
• CM: no
• Rank: $1$

Elliptic curves in class 312325.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
312325.o1	312325o2	\([0, -1, 1, -1281333, 557111943]\)	\(671088640/2197\)	\(761658432483203125\)	\([]\)	\(5443200\)	\(2.2966\)
312325.o2	312325o1	\([0, -1, 1, -80083, -8076182]\)	\(163840/13\)	\(4506854630078125\)	\([]\)	\(1814400\)	\(1.7473\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 312325.o have rank \(1\).

Complex multiplication

The elliptic curves in class 312325.o do not have complex multiplication.

Modular form 312325.2.a.o

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.