Elliptic curve isogeny class with Cremona label 33327g (LMFDB label 33327.n)

• Label: 33327g
• Number of curves: $4$
• Conductor: $33327$
• CM: no
• Rank: $1$

Elliptic curves in class 33327g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33327.n3	33327g1	\([1, -1, 0, -17556, -868213]\)	\(5545233/161\)	\(17374824256041\)	\([2]\)	\(84480\)	\(1.3183\)	\(\Gamma_0(N)\)-optimal
33327.n2	33327g2	\([1, -1, 0, -41361, 2012192]\)	\(72511713/25921\)	\(2797346705222601\)	\([2, 2]\)	\(168960\)	\(1.6648\)
33327.n4	33327g3	\([1, -1, 0, 125274, 14043239]\)	\(2014698447/1958887\)	\(-211399486723250847\)	\([2]\)	\(337920\)	\(2.0114\)
33327.n1	33327g4	\([1, -1, 0, -588876, 174041405]\)	\(209267191953/55223\)	\(5959564719822063\)	\([2]\)	\(337920\)	\(2.0114\)

Rank

The elliptic curves in class 33327g have rank \(1\).

Complex multiplication

The elliptic curves in class 33327g do not have complex multiplication.

Modular form 33327.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.