Elliptic curve isogeny class with LMFDB label 1045.b (Cremona label 1045b)

• Label: 1045.b
• Number of curves: $4$
• Conductor: $1045$
• CM: no
• Rank: $1$

Elliptic curves in class 1045.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1045.b1	1045b3	$[1, -1, 0, -1016789, -346894930]$	$116256292809537371612841/15216540068579856875$	$15216540068579856875$	$[4]$	$17664$	$2.4090$
1045.b2	1045b2	$[1, -1, 0, -982414, -374539305]$	$104859453317683374662841/2223652969140625$	$2223652969140625$	$[2, 2]$	$8832$	$2.0624$
1045.b3	1045b1	$[1, -1, 0, -982409, -374543312]$	$104857852278310619039721/47155625$	$47155625$	$[2]$	$4416$	$1.7158$	$\Gamma_0(N)$-optimal
1045.b4	1045b4	$[1, -1, 0, -948119, -401927292]$	$-94256762600623910012361/15323275604248046875$	$-15323275604248046875$	$[2]$	$17664$	$2.4090$

Rank

The elliptic curves in class 1045.b have rank $1$.

Complex multiplication

The elliptic curves in class 1045.b do not have complex multiplication.

Modular form 1045.2.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 LMFDB 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 LMFDB labels.