Elliptic curve isogeny class with Cremona label 156325i (LMFDB label 156325.i)

• Label: 156325i
• Number of curves: $3$
• Conductor: $156325$
• CM: no
• Rank: $2$

Elliptic curves in class 156325i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
156325.i3	156325i1	\([0, -1, 1, -14083, 642943]\)	\(4096000/37\)	\(2790498953125\)	\([]\)	\(207360\)	\(1.2107\)	\(\Gamma_0(N)\)-optimal
156325.i2	156325i2	\([0, -1, 1, -98583, -11503932]\)	\(1404928000/50653\)	\(3820193066828125\)	\([]\)	\(622080\)	\(1.7600\)
156325.i1	156325i3	\([0, -1, 1, -7914833, -8567952807]\)	\(727057727488000/37\)	\(2790498953125\)	\([]\)	\(1866240\)	\(2.3093\)

Rank

The elliptic curves in class 156325i have rank \(2\).

Complex multiplication

The elliptic curves in class 156325i do not have complex multiplication.

Modular form 156325.2.a.i

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.