Elliptic curve isogeny class with Cremona label 122304fi (LMFDB label 122304.da)

• Label: 122304fi
• Number of curves: $4$
• Conductor: $122304$
• CM: no
• Rank: $1$

Elliptic curves in class 122304fi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122304.da3	122304fi1	\([0, -1, 0, -22017, -1119327]\)	\(38272753/4368\)	\(134713398263808\)	\([2]\)	\(442368\)	\(1.4435\)	\(\Gamma_0(N)\)-optimal
122304.da2	122304fi2	\([0, -1, 0, -84737, 8326305]\)	\(2181825073/298116\)	\(9194189431504896\)	\([2, 2]\)	\(884736\)	\(1.7901\)
122304.da4	122304fi3	\([0, -1, 0, 134783, 44108065]\)	\(8780064047/32388174\)	\(-998883008951353344\)	\([2]\)	\(1769472\)	\(2.1367\)
122304.da1	122304fi4	\([0, -1, 0, -1307777, 576061473]\)	\(8020417344913/187278\)	\(5775836950560768\)	\([2]\)	\(1769472\)	\(2.1367\)

Rank

The elliptic curves in class 122304fi have rank \(1\).

Complex multiplication

The elliptic curves in class 122304fi do not have complex multiplication.

Modular form 122304.2.a.fi

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.