Elliptic curve isogeny class with Cremona label 11310d (LMFDB label 11310.e)

• Label: 11310d
• Number of curves: $4$
• Conductor: $11310$
• CM: no
• Rank: $1$

Elliptic curves in class 11310d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11310.e3	11310d1	\([1, 0, 1, -3864, 71062]\)	\(6377838054073849/1489533786000\)	\(1489533786000\)	\([2]\)	\(15360\)	\(1.0477\)	\(\Gamma_0(N)\)-optimal
11310.e2	11310d2	\([1, 0, 1, -20684, -1086154]\)	\(978581759592931129/58281773062500\)	\(58281773062500\)	\([2, 2]\)	\(30720\)	\(1.3943\)
11310.e1	11310d3	\([1, 0, 1, -326054, -71687698]\)	\(3833455222908263170009/14910644531250\)	\(14910644531250\)	\([2]\)	\(61440\)	\(1.7408\)
11310.e4	11310d4	\([1, 0, 1, 15566, -4479154]\)	\(417152543917888871/8913566138987250\)	\(-8913566138987250\)	\([2]\)	\(61440\)	\(1.7408\)

Rank

The elliptic curves in class 11310d have rank \(1\).

Complex multiplication

The elliptic curves in class 11310d do not have complex multiplication.

Modular form 11310.2.a.d

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.