# Properties

 Label 225.d Number of curves 2 Conductor 225 CM -3 Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("225.d1")

sage: E.isogeny_class()

## Elliptic curves in class 225.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
225.d1 225b2 [0, 0, 1, 0, -4219] [] 120
225.d2 225b1 [0, 0, 1, 0, 156]  40 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 225.d have rank $$0$$.

## Modular form225.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{4} + 5q^{7} + 5q^{13} + 4q^{16} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 