# Properties

 Label 38640.cu Number of curves $2$ Conductor $38640$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 38640.cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.cu1 38640cx2 $$[0, 1, 0, -11800, -3052]$$ $$44365623586201/25674468750$$ $$105162624000000$$ $$$$ $$110592$$ $$1.3800$$
38640.cu2 38640cx1 $$[0, 1, 0, -8120, 278100]$$ $$14457238157881/49990500$$ $$204761088000$$ $$$$ $$55296$$ $$1.0334$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 38640.cu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 38640.cu do not have complex multiplication.

## Modular form 38640.2.a.cu

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} + 2q^{11} - 6q^{13} + q^{15} - 6q^{19} + O(q^{20})$$ ## 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. 