# Properties

 Label 720.a Number of curves $2$ Conductor $720$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 720.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
720.a1 720a2 $$[0, 0, 0, -123, 522]$$ $$3721734/25$$ $$1382400$$ $$$$ $$128$$ $$0.012990$$
720.a2 720a1 $$[0, 0, 0, -3, 18]$$ $$-108/5$$ $$-138240$$ $$$$ $$64$$ $$-0.33358$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 720.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 720.a do not have complex multiplication.

## Modular form720.2.a.a

sage: E.q_eigenform(10)

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

## 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. 