# Properties

 Label 374790df Number of curves $2$ Conductor $374790$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("df1")

sage: E.isogeny_class()

## Elliptic curves in class 374790df

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374790.df2 374790df1 $$[1, 0, 0, 3824, 252956]$$ $$6967871/35100$$ $$-31151379203100$$ $$$$ $$1474560$$ $$1.2714$$ $$\Gamma_0(N)$$-optimal
374790.df1 374790df2 $$[1, 0, 0, -44226, 3203226]$$ $$10779215329/1232010$$ $$1093413410028810$$ $$$$ $$2949120$$ $$1.6180$$

## Rank

sage: E.rank()

The elliptic curves in class 374790df have rank $$1$$.

## Complex multiplication

The elliptic curves in class 374790df do not have complex multiplication.

## Modular form 374790.2.a.df

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} + q^{13} + 2q^{14} - q^{15} + q^{16} - 8q^{17} + q^{18} - 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 