Elliptic curve isogeny class with Cremona label 117600fd (LMFDB label 117600.dl)

• Label: 117600fd
• Number of curves: $4$
• Conductor: $117600$
• CM: no
• Rank: $1$

Elliptic curves in class 117600fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
117600.dl3	117600fd1	\([0, -1, 0, -6431658, 6278961312]\)	\(250094631024064/62015625\)	\(7296076265625000000\)	\([2, 2]\)	\(3538944\)	\(2.6071\)	\(\Gamma_0(N)\)-optimal
117600.dl4	117600fd2	\([0, -1, 0, -5666033, 7829351937]\)	\(-2671731885376/1969120125\)	\(-14826560869512000000000\)	\([2]\)	\(7077888\)	\(2.9536\)
117600.dl2	117600fd3	\([0, -1, 0, -7203408, 4678351812]\)	\(43919722445768/15380859375\)	\(14476341796875000000000\)	\([2]\)	\(7077888\)	\(2.9536\)
117600.dl1	117600fd4	\([0, -1, 0, -102900408, 401800836312]\)	\(128025588102048008/7875\)	\(7411887000000000\)	\([2]\)	\(7077888\)	\(2.9536\)

Rank

The elliptic curves in class 117600fd have rank \(1\).

Complex multiplication

The elliptic curves in class 117600fd do not have complex multiplication.

Modular form 117600.2.a.fd

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.