# Properties

 Label 94864.cw Number of curves $2$ Conductor $94864$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cw1")

sage: E.isogeny_class()

## Elliptic curves in class 94864.cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94864.cw1 94864cr2 [0, -1, 0, -2847896, 1850854832] [] 1520640
94864.cw2 94864cr1 [0, -1, 0, -1976, -131536] [] 138240 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 94864.cw have rank $$0$$.

## Complex multiplication

The elliptic curves in class 94864.cw do not have complex multiplication.

## Modular form 94864.2.a.cw

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + q^{9} - q^{13} - 2q^{15} + 5q^{17} + 6q^{19} + O(q^{20})$$

## 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. 