Elliptic curve isogeny class with Cremona label 2299d (LMFDB label 2299.b)

• Label: 2299d
• Number of curves: $3$
• Conductor: $2299$
• CM: no
• Rank: $0$

Elliptic curves in class 2299d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2299.b3	2299d1	$[0, 1, 1, 81, 39]$	$32768/19$	$-33659659$	$[]$	$450$	$0.13377$	$\Gamma_0(N)$-optimal
2299.b2	2299d2	$[0, 1, 1, -1129, 15164]$	$-89915392/6859$	$-12151136899$	$[]$	$1350$	$0.68308$
2299.b1	2299d3	$[0, 1, 1, -93089, 10900929]$	$-50357871050752/19$	$-33659659$	$[]$	$4050$	$1.2324$

Rank

The elliptic curves in class 2299d have rank $0$.

Complex multiplication

The elliptic curves in class 2299d do not have complex multiplication.

Modular form 2299.2.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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.