Elliptic curve isogeny class with Cremona label 99b (LMFDB label 99.b)

• Label: 99b
• Number of curves: $4$
• Conductor: $99$
• CM: no
• Rank: $0$

Elliptic curves in class 99b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
99.b3	99b1	\([1, -1, 1, -59, 186]\)	\(30664297/297\)	\(216513\)	\([4]\)	\(12\)	\(-0.15647\)	\(\Gamma_0(N)\)-optimal
99.b2	99b2	\([1, -1, 1, -104, -102]\)	\(169112377/88209\)	\(64304361\)	\([2, 2]\)	\(24\)	\(0.19010\)
99.b1	99b3	\([1, -1, 1, -1319, -18084]\)	\(347873904937/395307\)	\(288178803\)	\([2]\)	\(48\)	\(0.53667\)
99.b4	99b4	\([1, -1, 1, 391, -1092]\)	\(9090072503/5845851\)	\(-4261625379\)	\([2]\)	\(48\)	\(0.53667\)

Rank

The elliptic curves in class 99b have rank \(0\).

Complex multiplication

The elliptic curves in class 99b do not have complex multiplication.

Modular form 99.2.a.b

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.