Elliptic curve isogeny class with Cremona label 57330cm (LMFDB label 57330.bu)

• Label: 57330cm
• Number of curves: $6$
• Conductor: $57330$
• CM: no
• Rank: $2$

Elliptic curves in class 57330cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57330.bu6	57330cm1	$[1, -1, 0, 6606, 81108]$	$371694959/249600$	$-21407223801600$	$[2]$	$196608$	$1.2466$	$\Gamma_0(N)$-optimal
57330.bu5	57330cm2	$[1, -1, 0, -28674, 694980]$	$30400540561/15210000$	$1304502700410000$	$[2, 2]$	$393216$	$1.5932$
57330.bu3	57330cm3	$[1, -1, 0, -249174, -47329920]$	$19948814692561/231344100$	$19841486073236100$	$[2, 2]$	$786432$	$1.9398$
57330.bu2	57330cm4	$[1, -1, 0, -372654, 87584328]$	$66730743078481/60937500$	$5226372998437500$	$[2]$	$786432$	$1.9398$
57330.bu4	57330cm5	$[1, -1, 0, -50724, -120796110]$	$-168288035761/73415764890$	$-6296585374863291690$	$[2]$	$1572864$	$2.2863$
57330.bu1	57330cm6	$[1, -1, 0, -3975624, -3050103330]$	$81025909800741361/11088090$	$950982468598890$	$[2]$	$1572864$	$2.2863$

Rank

The elliptic curves in class 57330cm have rank $2$.

Complex multiplication

The elliptic curves in class 57330cm do not have complex multiplication.

Modular form 57330.2.a.cm

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.