Elliptic curve isogeny class with Cremona label 27930g (LMFDB label 27930.g)

• Label: 27930g
• Number of curves: $4$
• Conductor: $27930$
• CM: no
• Rank: $1$

Elliptic curves in class 27930g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27930.g3	27930g1	\([1, 1, 0, -645698, 199409652]\)	\(253060782505556761/41184460800\)	\(4845310628659200\)	\([2]\)	\(294912\)	\(2.0187\)	\(\Gamma_0(N)\)-optimal
27930.g2	27930g2	\([1, 1, 0, -708418, 158252788]\)	\(334199035754662681/101099003040000\)	\(11894196608652960000\)	\([2, 2]\)	\(589824\)	\(2.3653\)
27930.g4	27930g3	\([1, 1, 0, 1937582, 1064772388]\)	\(6837784281928633319/8113766016106800\)	\(-954576458028948913200\)	\([2]\)	\(1179648\)	\(2.7119\)
27930.g1	27930g4	\([1, 1, 0, -4357938, -3381051708]\)	\(77799851782095807001/3092322318750000\)	\(363808628478618750000\)	\([2]\)	\(1179648\)	\(2.7119\)

Rank

The elliptic curves in class 27930g have rank \(1\).

Complex multiplication

The elliptic curves in class 27930g do not have complex multiplication.

Modular form 27930.2.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.