# Properties

 Label 324870fl Number of curves 2 Conductor 324870 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("324870.fl1")

sage: E.isogeny_class()

## Elliptic curves in class 324870fl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
324870.fl1 324870fl1 [1, 0, 0, -667381, -207513055] [2] 5529600 $$\Gamma_0(N)$$-optimal
324870.fl2 324870fl2 [1, 0, 0, -102901, -547217119] [2] 11059200

## Rank

sage: E.rank()

The elliptic curves in class 324870fl have rank $$0$$.

## Modular form 324870.2.a.fl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + q^{12} + q^{13} - q^{15} + q^{16} + q^{17} + q^{18} - 2q^{19} + O(q^{20})$$

## 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.