# Properties

 Label 54720co Number of curves $4$ Conductor $54720$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54720.eu1")

sage: E.isogeny_class()

## Elliptic curves in class 54720co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54720.eu4 54720co1 [0, 0, 0, -5772, -288016] [2] 147456 $$\Gamma_0(N)$$-optimal
54720.eu3 54720co2 [0, 0, 0, -109452, -13932304] [2, 2] 294912
54720.eu2 54720co3 [0, 0, 0, -126732, -9239056] [4] 589824
54720.eu1 54720co4 [0, 0, 0, -1751052, -891859984] [2] 589824

## Rank

sage: E.rank()

The elliptic curves in class 54720co have rank $$0$$.

## Modular form 54720.2.a.eu

sage: E.q_eigenform(10)

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

## 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.