# Properties

 Label 54720dj Number of curves $4$ Conductor $54720$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54720.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 54720dj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54720.bb3 54720dj1 [0, 0, 0, -17868, 913808]  98304 $$\Gamma_0(N)$$-optimal
54720.bb2 54720dj2 [0, 0, 0, -29388, -408688] [2, 2] 196608
54720.bb4 54720dj3 [0, 0, 0, 114612, -3231088]  393216
54720.bb1 54720dj4 [0, 0, 0, -357708, -82226032]  393216

## Rank

sage: E.rank()

The elliptic curves in class 54720dj have rank $$1$$.

## Modular form 54720.2.a.bb

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 