# Properties

 Label 248430.cu Number of curves $2$ Conductor $248430$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cu1")

sage: E.isogeny_class()

## Elliptic curves in class 248430.cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.cu1 248430cu2 $$[1, 0, 1, -381099, 81087892]$$ $$10779215329/1232010$$ $$699620597207032410$$ $$[2]$$ $$5806080$$ $$2.1564$$
248430.cu2 248430cu1 $$[1, 0, 1, 32951, 6393272]$$ $$6967871/35100$$ $$-19932210746639100$$ $$[2]$$ $$2903040$$ $$1.8098$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 248430.cu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 248430.cu do not have complex multiplication.

## Modular form 248430.2.a.cu

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.