# Properties

 Label 272.a Number of curves $2$ Conductor $272$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 272.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272.a1 272a2 $$[0, 1, 0, -48, -140]$$ $$6097250/289$$ $$591872$$ $$$$ $$32$$ $$-0.13184$$
272.a2 272a1 $$[0, 1, 0, -8, 4]$$ $$62500/17$$ $$17408$$ $$$$ $$16$$ $$-0.47842$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 272.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 272.a do not have complex multiplication.

## Modular form272.2.a.a

sage: E.q_eigenform(10)

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

## 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. 