# Properties

 Label 55488bl Number of curves 6 Conductor 55488 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55488.cr1")

sage: E.isogeny_class()

## Elliptic curves in class 55488bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55488.cr5 55488bl1 [0, 1, 0, -629249, 177971295] [2] 884736 $$\Gamma_0(N)$$-optimal
55488.cr4 55488bl2 [0, 1, 0, -2108929, -972923809] [2, 2] 1769472
55488.cr6 55488bl3 [0, 1, 0, 4179711, -5660476065] [2] 3538944
55488.cr2 55488bl4 [0, 1, 0, -32072449, -69918983329] [2, 2] 3538944
55488.cr3 55488bl5 [0, 1, 0, -30407809, -77498755105] [2] 7077888
55488.cr1 55488bl6 [0, 1, 0, -513153409, -4474407604513] [2] 7077888

## Rank

sage: E.rank()

The elliptic curves in class 55488bl have rank $$2$$.

## Modular form 55488.2.a.cr

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{9} - 4q^{11} + 2q^{13} - 2q^{15} - 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().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.

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

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.