Elliptic curve isogeny class with Cremona label 45084h (LMFDB label 45084.f)

• Label: 45084h
• Number of curves: $4$
• Conductor: $45084$
• CM: no
• Rank: $1$

Elliptic curves in class 45084h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
45084.f2	45084h1	$[0, -1, 0, -911313, 335149650]$	$216727177216000/2738853$	$1057748052293712$	$[2]$	$414720$	$2.0292$	$\Gamma_0(N)$-optimal
45084.f3	45084h2	$[0, -1, 0, -886748, 354045048]$	$-12479332642000/1526829993$	$-9434614862670596352$	$[2]$	$829440$	$2.3758$
45084.f1	45084h3	$[0, -1, 0, -1431513, -88511634]$	$840033089536000/477272151837$	$184323031947905028048$	$[2]$	$1244160$	$2.5785$
45084.f4	45084h4	$[0, -1, 0, 5667772, -710409000]$	$3258571509326000/1920843121977$	$-11869307749093185001728$	$[2]$	$2488320$	$2.9251$

Rank

The elliptic curves in class 45084h have rank $1$.

Complex multiplication

The elliptic curves in class 45084h do not have complex multiplication.

Modular form 45084.2.a.h

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.

$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.