# Properties

 Label 63426.e Number of curves 4 Conductor 63426 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("63426.e1")

sage: E.isogeny_class()

## Elliptic curves in class 63426.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63426.e1 63426e3 [1, 1, 0, -77380, 8221072]  345600
63426.e2 63426e4 [1, 1, 0, -38940, 16439544]  691200
63426.e3 63426e1 [1, 1, 0, -5305, -142511]  115200 $$\Gamma_0(N)$$-optimal
63426.e4 63426e2 [1, 1, 0, 4305, -590337]  230400

## Rank

sage: E.rank()

The elliptic curves in class 63426.e have rank $$1$$.

## Modular form 63426.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} + 2q^{7} - q^{8} + q^{9} + q^{11} - q^{12} + 4q^{13} - 2q^{14} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 