# Properties

 Label 272d Number of curves 4 Conductor 272 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("272.d1")

sage: E.isogeny_class()

## Elliptic curves in class 272d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
272.d4 272d1 [0, -1, 0, -48, -64]  48 $$\Gamma_0(N)$$-optimal
272.d3 272d2 [0, -1, 0, -688, -6720]  96
272.d2 272d3 [0, -1, 0, -1648, 26304]  144
272.d1 272d4 [0, -1, 0, -1808, 21056]  288

## Rank

sage: E.rank()

The elliptic curves in class 272d have rank $$0$$.

## Modular form272.2.a.d

sage: E.q_eigenform(10)

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

## 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. 