# Properties

 Label 134640.fd Number of curves $2$ Conductor $134640$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fd1")

sage: E.isogeny_class()

## Elliptic curves in class 134640.fd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
134640.fd1 134640be2 [0, 0, 0, -20667, 730474]  393216
134640.fd2 134640be1 [0, 0, 0, 3813, 79306]  196608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 134640.fd have rank $$1$$.

## Complex multiplication

The elliptic curves in class 134640.fd do not have complex multiplication.

## Modular form 134640.2.a.fd

sage: E.q_eigenform(10)

$$q + q^{5} + 2q^{7} + q^{11} - q^{17} + O(q^{20})$$

## 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. 