# Properties

 Label 64009.c Number of curves $2$ Conductor $64009$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 64009.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
64009.c1 64009b2 [1, 1, 0, -1921603, -1026119574] [] 830544
64009.c2 64009b1 [1, 1, 0, -1333, 72714] [] 75504 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 64009.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 64009.c do not have complex multiplication.

## Modular form 64009.2.a.c

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 