Elliptic curve isogeny class with LMFDB label 6552.e (Cremona label 6552h)

• Label: 6552.e
• Number of curves: $4$
• Conductor: $6552$
• CM: no
• Rank: $1$

Elliptic curves in class 6552.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6552.e1	6552h4	$[0, 0, 0, -122331, 16468454]$	$271210066309732/51597$	$38516954112$	$[2]$	$16384$	$1.4233$
6552.e2	6552h3	$[0, 0, 0, -14691, -285010]$	$469732169092/224827239$	$167832634604544$	$[2]$	$16384$	$1.4233$
6552.e3	6552h2	$[0, 0, 0, -7671, 255530]$	$267492843088/3651921$	$681536104704$	$[2, 2]$	$8192$	$1.0768$
6552.e4	6552h1	$[0, 0, 0, -66, 10649]$	$-2725888/4198467$	$-48970919088$	$[4]$	$4096$	$0.73019$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 6552.e have rank $1$.

Complex multiplication

The elliptic curves in class 6552.e do not have complex multiplication.

Modular form 6552.2.a.e

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.

$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.