# Properties

 Label 67760bo Number of curves $3$ Conductor $67760$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bo1")

sage: E.isogeny_class()

## Elliptic curves in class 67760bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67760.k2 67760bo1 $$[0, -1, 0, -2581, 56861]$$ $$-262144/35$$ $$-253970984960$$ $$[]$$ $$64800$$ $$0.92094$$ $$\Gamma_0(N)$$-optimal
67760.k3 67760bo2 $$[0, -1, 0, 16779, -148355]$$ $$71991296/42875$$ $$-311114456576000$$ $$[]$$ $$194400$$ $$1.4703$$
67760.k1 67760bo3 $$[0, -1, 0, -254261, -51537539]$$ $$-250523582464/13671875$$ $$-99207416000000000$$ $$[]$$ $$583200$$ $$2.0196$$

## Rank

sage: E.rank()

The elliptic curves in class 67760bo have rank $$0$$.

## Complex multiplication

The elliptic curves in class 67760bo do not have complex multiplication.

## Modular form 67760.2.a.bo

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} - 2q^{9} - 5q^{13} + q^{15} - 3q^{17} + 2q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 