# Properties

 Label 395798o Number of curves 3 Conductor 395798 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("395798.o1")

sage: E.isogeny_class()

## Elliptic curves in class 395798o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
395798.o2 395798o1 [1, 0, 0, -6016488, 6413883904] [] 18724608 $$\Gamma_0(N)$$-optimal
395798.o3 395798o2 [1, 0, 0, 40395137, -23819391207] [] 56173824
395798.o1 395798o3 [1, 0, 0, -641366918, -6492323742620] [] 168521472

## Rank

sage: E.rank()

The elliptic curves in class 395798o have rank $$1$$.

## Modular form 395798.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{7} + q^{8} + q^{9} - 3q^{11} - 2q^{12} + q^{14} + q^{16} - 3q^{17} + q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 