# Properties

 Label 63525q Number of curves 4 Conductor 63525 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("63525.bw1")

sage: E.isogeny_class()

## Elliptic curves in class 63525q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63525.bw3 63525q1 [1, 1, 0, -7625, -246000] [2] 138240 $$\Gamma_0(N)$$-optimal
63525.bw2 63525q2 [1, 1, 0, -22750, 1009375] [2, 2] 276480
63525.bw4 63525q3 [1, 1, 0, 52875, 6378750] [2] 552960
63525.bw1 63525q4 [1, 1, 0, -340375, 76286500] [2] 552960

## Rank

sage: E.rank()

The elliptic curves in class 63525q have rank $$1$$.

## Modular form 63525.2.a.bw

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.