# Properties

 Label 180.a Number of curves 4 Conductor 180 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("180.a1")

sage: E.isogeny_class()

## Elliptic curves in class 180.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
180.a1 180a3 [0, 0, 0, -372, 2761]  36
180.a2 180a4 [0, 0, 0, -327, 3454]  72
180.a3 180a1 [0, 0, 0, -12, -11]  12 $$\Gamma_0(N)$$-optimal
180.a4 180a2 [0, 0, 0, 33, -74]  24

## Rank

sage: E.rank()

The elliptic curves in class 180.a have rank $$0$$.

## Modular form180.2.a.a

sage: E.q_eigenform(10)

$$q + q^{5} + 2q^{7} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 