# Properties

 Label 270.a Number of curves 2 Conductor 270 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("270.a1")

sage: E.isogeny_class()

## Elliptic curves in class 270.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
270.a1 270a1 [1, -1, 0, -15, 35]  36 $$\Gamma_0(N)$$-optimal
270.a2 270a2 [1, -1, 0, 120, -424] [] 108

## Rank

sage: E.rank()

The elliptic curves in class 270.a have rank $$0$$.

## Modular form270.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + 2q^{7} - q^{8} + q^{10} + 3q^{11} - q^{13} - 2q^{14} + q^{16} + 3q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 