# Properties

 Label 44880by Number of curves 2 Conductor 44880 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("44880.bf1")

sage: E.isogeny_class()

## Elliptic curves in class 44880by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44880.bf2 44880by1 [0, -1, 0, -14080, -278528]  129024 $$\Gamma_0(N)$$-optimal
44880.bf1 44880by2 [0, -1, 0, -188160, -31334400]  258048

## Rank

sage: E.rank()

The elliptic curves in class 44880by have rank $$1$$.

## Modular form 44880.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 2q^{7} + q^{9} + q^{11} - 4q^{13} - q^{15} + q^{17} + 6q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 