Elliptic curve isogeny class with Cremona label 99705j (LMFDB label 99705.m)

• Label: 99705j
• Number of curves: $4$
• Conductor: $99705$
• CM: no
• Rank: $1$

Elliptic curves in class 99705j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
99705.m4	99705j1	\([1, 1, 0, 131923, 11665416]\)	\(10519294081031/8500170375\)	\(-205173448938318375\)	\([2]\)	\(1536000\)	\(2.0097\)	\(\Gamma_0(N)\)-optimal
99705.m3	99705j2	\([1, 1, 0, -632482, 100795039]\)	\(1159246431432649/488076890625\)	\(11780989624766390625\)	\([2, 2]\)	\(3072000\)	\(2.3563\)
99705.m2	99705j3	\([1, 1, 0, -4786857, -3963014586]\)	\(502552788401502649/10024505152875\)	\(241967184818375860875\)	\([2]\)	\(6144000\)	\(2.7029\)
99705.m1	99705j4	\([1, 1, 0, -8708587, 9884188636]\)	\(3026030815665395929/1364501953125\)	\(32935760044189453125\)	\([2]\)	\(6144000\)	\(2.7029\)

Rank

The elliptic curves in class 99705j have rank \(1\).

Complex multiplication

The elliptic curves in class 99705j do not have complex multiplication.

Modular form 99705.2.a.j

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.