# Properties

 Label 379050bi Number of curves $2$ Conductor $379050$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 379050bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.bi2 379050bi1 $$[1, 1, 0, -262815, -97319835]$$ $$-1706927698345/2483133408$$ $$-2920529970497311200$$ $$[]$$ $$8640000$$ $$2.2352$$ $$\Gamma_0(N)$$-optimal
379050.bi1 379050bi2 $$[1, 1, 0, -5645325, 11713195875]$$ $$-43308090025/103996158$$ $$-47779207751222636718750$$ $$[]$$ $$43200000$$ $$3.0399$$

## Rank

sage: E.rank()

The elliptic curves in class 379050bi have rank $$1$$.

## Complex multiplication

The elliptic curves in class 379050bi do not have complex multiplication.

## Modular form 379050.2.a.bi

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 