# Properties

 Label 277350.bu Number of curves $2$ Conductor $277350$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bu1")

sage: E.isogeny_class()

## Elliptic curves in class 277350.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.bu1 277350bu2 $$[1, 0, 1, -44501, 4223648]$$ $$-337335507529/72000000$$ $$-2080125000000000$$ $$[]$$ $$1741824$$ $$1.6606$$
277350.bu2 277350bu1 $$[1, 0, 1, 3874, -33352]$$ $$222641831/145800$$ $$-4212253125000$$ $$[]$$ $$580608$$ $$1.1113$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 277350.bu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 277350.bu do not have complex multiplication.

## Modular form 277350.2.a.bu

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + 2q^{7} - q^{8} + q^{9} - 3q^{11} + q^{12} + 4q^{13} - 2q^{14} + q^{16} + 3q^{17} - q^{18} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.