# Properties

 Label 55440ec Number of curves 4 Conductor 55440 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55440.cv1")

sage: E.isogeny_class()

## Elliptic curves in class 55440ec

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55440.cv3 55440ec1 [0, 0, 0, -8067, 5427074]  331776 $$\Gamma_0(N)$$-optimal
55440.cv2 55440ec2 [0, 0, 0, -514947, 140966786]  663552
55440.cv4 55440ec3 [0, 0, 0, 72573, -146192254]  995328
55440.cv1 55440ec4 [0, 0, 0, -3760707, -2727523006]  1990656

## Rank

sage: E.rank()

The elliptic curves in class 55440ec have rank $$0$$.

## Modular form 55440.2.a.cv

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - q^{11} - 4q^{13} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 