Elliptic curve isogeny class with Cremona label 90459r (LMFDB label 90459.f)

• Label: 90459r
• Number of curves: $4$
• Conductor: $90459$
• CM: no
• Rank: $0$

Elliptic curves in class 90459r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
90459.f3	90459r1	$[1, -1, 1, -7241, -203128]$	$389017/57$	$6151335295617$	$[2]$	$147840$	$1.1789$	$\Gamma_0(N)$-optimal
90459.f2	90459r2	$[1, -1, 1, -31046, 1910756]$	$30664297/3249$	$350626111850169$	$[2, 2]$	$295680$	$1.5255$
90459.f4	90459r3	$[1, -1, 1, 40369, 9366482]$	$67419143/390963$	$-42192008792637003$	$[2]$	$591360$	$1.8720$
90459.f1	90459r4	$[1, -1, 1, -483341, 129457946]$	$115714886617/1539$	$166086052981659$	$[2]$	$591360$	$1.8720$

Rank

The elliptic curves in class 90459r have rank $0$.

Complex multiplication

The elliptic curves in class 90459r do not have complex multiplication.

Modular form 90459.2.a.r

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.