# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("73920.di1")

sage: E.isogeny_class()

## Elliptic curves in class 73920.di

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.di1 73920ft4 [0, -1, 0, -2111425, -1180177823] [2] 1179648
73920.di2 73920ft2 [0, -1, 0, -135745, -17292575] [2, 2] 589824
73920.di3 73920ft1 [0, -1, 0, -32065, 1929697] [2] 294912 $$\Gamma_0(N)$$-optimal
73920.di4 73920ft3 [0, -1, 0, 181055, -86291615] [4] 1179648

## Rank

sage: E.rank()

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

## Modular form 73920.2.a.di

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.