Elliptic curve isogeny class with Cremona label 97344fn (LMFDB label 97344.ci)

• Label: 97344fn
• Number of curves: $4$
• Conductor: $97344$
• CM: no
• Rank: $1$

Elliptic curves in class 97344fn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
97344.ci4	97344fn1	\([0, 0, 0, -1900236, 21049193360]\)	\(-822656953/207028224\)	\(-190966470161441872674816\)	\([2]\)	\(10321920\)	\(3.1464\)	\(\Gamma_0(N)\)-optimal
97344.ci3	97344fn2	\([0, 0, 0, -126500556, 542626132880]\)	\(242702053576633/2554695936\)	\(2356496403281229983514624\)	\([2, 2]\)	\(20643840\)	\(3.4930\)
97344.ci2	97344fn3	\([0, 0, 0, -227738316, -448653517936]\)	\(1416134368422073/725251155408\)	\(668984404410352640848822272\)	\([2]\)	\(41287680\)	\(3.8396\)
97344.ci1	97344fn4	\([0, 0, 0, -2018867916, 34914829912976]\)	\(986551739719628473/111045168\)	\(102430013414230418522112\)	\([2]\)	\(41287680\)	\(3.8396\)

Rank

The elliptic curves in class 97344fn have rank \(1\).

Complex multiplication

The elliptic curves in class 97344fn do not have complex multiplication.

Modular form 97344.2.a.fn

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.