Elliptic curve isogeny class with Cremona label 28749a (LMFDB label 28749.a)

• Label: 28749a
• Number of curves: $4$
• Conductor: $28749$
• CM: no
• Rank: $1$

Elliptic curves in class 28749a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28749.a3	28749a1	$[1, 1, 1, -22617, 1297998]$	$498677257/777$	$1993569419793$	$[4]$	$65664$	$1.2588$	$\Gamma_0(N)$-optimal
28749.a2	28749a2	$[1, 1, 1, -29462, 438266]$	$1102302937/603729$	$1549003439179161$	$[2, 2]$	$131328$	$1.6054$
28749.a4	28749a3	$[1, 1, 1, 114283, 3600656]$	$64336588343/39357381$	$-100980271820774829$	$[2]$	$262656$	$1.9520$
28749.a1	28749a4	$[1, 1, 1, -282727, -57610072]$	$974126411497/7195797$	$18462446396702973$	$[2]$	$262656$	$1.9520$

Rank

The elliptic curves in class 28749a have rank $1$.

Complex multiplication

The elliptic curves in class 28749a do not have complex multiplication.

Modular form 28749.2.a.a

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.