# Properties

 Label 63580d Number of curves 4 Conductor 63580 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("63580.m1")

sage: E.isogeny_class()

## Elliptic curves in class 63580d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63580.m4 63580d1 [0, -1, 0, -13101, 569726] [2] 186624 $$\Gamma_0(N)$$-optimal
63580.m3 63580d2 [0, -1, 0, -28996, -1064280] [2] 373248
63580.m2 63580d3 [0, -1, 0, -128701, -17504334] [2] 559872
63580.m1 63580d4 [0, -1, 0, -2051996, -1130707480] [2] 1119744

## Rank

sage: E.rank()

The elliptic curves in class 63580d have rank $$1$$.

## Modular form 63580.2.a.m

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + 4q^{7} + q^{9} + q^{11} - 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.