# Properties

 Label 73920.hc Number of curves 4 Conductor 73920 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("73920.hc1")

sage: E.isogeny_class()

## Elliptic curves in class 73920.hc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.hc1 73920dj4 [0, 1, 0, -2111425, 1180177823] [4] 1179648
73920.hc2 73920dj2 [0, 1, 0, -135745, 17292575] [2, 2] 589824
73920.hc3 73920dj1 [0, 1, 0, -32065, -1929697] [2] 294912 $$\Gamma_0(N)$$-optimal
73920.hc4 73920dj3 [0, 1, 0, 181055, 86291615] [2] 1179648

## Rank

sage: E.rank()

The elliptic curves in class 73920.hc have rank $$0$$.

## Modular form 73920.2.a.hc

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} + q^{11} - 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.