# Properties

 Label 132.a Number of curves 2 Conductor 132 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("132.a1")

sage: E.isogeny_class()

## Elliptic curves in class 132.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
132.a1 132b2 [0, -1, 0, -1292, 18312]  60
132.a2 132b1 [0, -1, 0, -77, 330]  30 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 132.a have rank $$0$$.

## Modular form132.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + 2q^{7} + q^{9} - q^{11} + 6q^{13} - 2q^{15} - 4q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 