Elliptic curve isogeny class with Cremona label 12705e (LMFDB label 12705.c)

• Label: 12705e
• Number of curves: $4$
• Conductor: $12705$
• CM: no
• Rank: $1$

Elliptic curves in class 12705e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12705.c3	12705e1	\([1, 1, 1, -1965345, 1059670470]\)	\(473897054735271721/779625\)	\(1381153244625\)	\([4]\)	\(138240\)	\(2.0213\)	\(\Gamma_0(N)\)-optimal
12705.c2	12705e2	\([1, 1, 1, -1965950, 1058984642]\)	\(474334834335054841/607815140625\)	\(1076781598340765625\)	\([2, 2]\)	\(276480\)	\(2.3679\)
12705.c1	12705e3	\([1, 1, 1, -2505005, 431309000]\)	\(981281029968144361/522287841796875\)	\(925264771301513671875\)	\([2]\)	\(552960\)	\(2.7144\)
12705.c4	12705e4	\([1, 1, 1, -1436575, 1642779392]\)	\(-185077034913624841/551466161890875\)	\(-976955945225560405875\)	\([2]\)	\(552960\)	\(2.7144\)

Rank

The elliptic curves in class 12705e have rank \(1\).

Complex multiplication

The elliptic curves in class 12705e do not have complex multiplication.

Modular form 12705.2.a.e

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.