# Properties

 Label 44880.cc Number of curves $2$ Conductor $44880$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

## Elliptic curves in class 44880.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44880.cc1 44880cc2 [0, 1, 0, -2296, -27820]  49152
44880.cc2 44880cc1 [0, 1, 0, 424, -2796]  24576 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 44880.cc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 44880.cc do not have complex multiplication.

## Modular form 44880.2.a.cc

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 2q^{7} + q^{9} - q^{11} - q^{15} + q^{17} + O(q^{20})$$

## 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. 