# Properties

 Label 115920.co Number of curves $2$ Conductor $115920$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.co1 115920ee1 $$[0, 0, 0, -543587547, -4875769801334]$$ $$5949010462538271898545049/3314625947988102720$$ $$9897420046677306912276480$$ $$$$ $$40734720$$ $$3.7436$$ $$\Gamma_0(N)$$-optimal
115920.co2 115920ee2 $$[0, 0, 0, -446779227, -6667362656246]$$ $$-3303050039017428591035929/4519896503737558217400$$ $$-13496338641816289036224921600$$ $$$$ $$81469440$$ $$4.0902$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.co have rank $$0$$.

## Complex multiplication

The elliptic curves in class 115920.co do not have complex multiplication.

## Modular form 115920.2.a.co

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 