# Properties

 Label 8925.v Number of curves 4 Conductor 8925 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8925.v1")

sage: E.isogeny_class()

## Elliptic curves in class 8925.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8925.v1 8925d4 [1, 1, 0, -42150, 3313125]  24576
8925.v2 8925d3 [1, 1, 0, -13400, -560625]  24576
8925.v3 8925d2 [1, 1, 0, -2775, 45000] [2, 2] 12288
8925.v4 8925d1 [1, 1, 0, 350, 4375]  6144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8925.v have rank $$0$$.

## Modular form8925.2.a.v

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 