# Properties

 Label 73920dc Number of curves $4$ Conductor $73920$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dc1")

sage: E.isogeny_class()

## Elliptic curves in class 73920dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.gq4 73920dc1 $$[0, 1, 0, 1455, 20943]$$ $$20777545136/23059575$$ $$-377808076800$$ $$[2]$$ $$65536$$ $$0.90798$$ $$\Gamma_0(N)$$-optimal
73920.gq3 73920dc2 $$[0, 1, 0, -8225, 189375]$$ $$939083699236/300155625$$ $$19670999040000$$ $$[2, 2]$$ $$131072$$ $$1.2545$$
73920.gq2 73920dc3 $$[0, 1, 0, -52225, -4465825]$$ $$120186986927618/4332064275$$ $$567812328652800$$ $$[2]$$ $$262144$$ $$1.6011$$
73920.gq1 73920dc4 $$[0, 1, 0, -119105, 15779103]$$ $$1425631925916578/270703125$$ $$35481600000000$$ $$[2]$$ $$262144$$ $$1.6011$$

## Rank

sage: E.rank()

The elliptic curves in class 73920dc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 73920dc do not have complex multiplication.

## Modular form 73920.2.a.dc

sage: E.q_eigenform(10)

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

## 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.