# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 379050.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.f1 379050f1 $$[1, 1, 0, -1096725, 747550125]$$ $$-549754417/592704$$ $$-157284777322701000000$$ $$[]$$ $$13296960$$ $$2.5703$$ $$\Gamma_0(N)$$-optimal
379050.f2 379050f2 $$[1, 1, 0, 9191775, -13502022375]$$ $$323648023823/484243284$$ $$-128502755328044791312500$$ $$[]$$ $$39890880$$ $$3.1196$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 379050.2.a.f

sage: E.q_eigenform(10)

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