# Properties

 Label 259920er Number of curves $2$ Conductor $259920$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("259920.er1")

sage: E.isogeny_class()

## Elliptic curves in class 259920er

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259920.er2 259920er1 [0, 0, 0, -11749467, 15960934154]  14008320 $$\Gamma_0(N)$$-optimal
259920.er1 259920er2 [0, 0, 0, -189534747, 1004340419786]  28016640

## Rank

sage: E.rank()

The elliptic curves in class 259920er have rank $$0$$.

## Modular form 259920.2.a.er

sage: E.q_eigenform(10)

$$q + q^{5} - 2q^{7} + 2q^{13} + 6q^{17} + O(q^{20})$$

## 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 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. 