# Properties

 Label 67760.cd Number of curves 4 Conductor 67760 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("67760.cd1")

sage: E.isogeny_class()

## Elliptic curves in class 67760.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67760.cd1 67760bt4 [0, -1, 0, -50560616, -134439928720]  9953280
67760.cd2 67760bt2 [0, -1, 0, -6923176, 6951448176]  3317760
67760.cd3 67760bt1 [0, -1, 0, -108456, 267570800]  1658880 $$\Gamma_0(N)$$-optimal
67760.cd4 67760bt3 [0, -1, 0, 975704, -7207061904]  4976640

## Rank

sage: E.rank()

The elliptic curves in class 67760.cd have rank $$0$$.

## Modular form 67760.2.a.cd

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + q^{7} + q^{9} + 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 