# Properties

 Label 73920.eg Number of curves $2$ Conductor $73920$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("eg1")

sage: E.isogeny_class()

## Elliptic curves in class 73920.eg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.eg1 73920ga2 $$[0, -1, 0, -2065, -35375]$$ $$59466754384/121275$$ $$1986969600$$ $$$$ $$61440$$ $$0.67064$$
73920.eg2 73920ga1 $$[0, -1, 0, -85, -923]$$ $$-67108864/343035$$ $$-351267840$$ $$$$ $$30720$$ $$0.32407$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 73920.2.a.eg

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} + q^{11} + 6q^{13} - q^{15} + 2q^{17} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 