# Properties

 Label 720i Number of curves 4 Conductor 720 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("720.h1")

sage: E.isogeny_class()

## Elliptic curves in class 720i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.h3 720i1 [0, 0, 0, -12, 11]  48 $$\Gamma_0(N)$$-optimal
720.h4 720i2 [0, 0, 0, 33, 74]  96
720.h1 720i3 [0, 0, 0, -372, -2761]  144
720.h2 720i4 [0, 0, 0, -327, -3454]  288

## Rank

sage: E.rank()

The elliptic curves in class 720i have rank $$0$$.

## Modular form720.2.a.h

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 Cremona 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 Cremona labels. 