# Properties

 Label 26928bd Number of curves $2$ Conductor $26928$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 26928bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26928.r2 26928bd1 [0, 0, 0, -1731, 22466] [2] 18432 $$\Gamma_0(N)$$-optimal
26928.r1 26928bd2 [0, 0, 0, -26211, 1633250] [2] 36864

## Rank

sage: E.rank()

The elliptic curves in class 26928bd have rank $$1$$.

## Complex multiplication

The elliptic curves in class 26928bd do not have complex multiplication.

## Modular form 26928.2.a.bd

sage: E.q_eigenform(10)

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

## 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.