# Properties

 Label 265200.w Number of curves 2 Conductor 265200 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.w1")

sage: E.isogeny_class()

## Elliptic curves in class 265200.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.w1 265200w2 [0, -1, 0, -1183208, 495776112] [] 2115072
265200.w2 265200w1 [0, -1, 0, -13208, 819312] [] 705024 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 265200.w have rank $$2$$.

## Modular form 265200.2.a.w

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} - 3q^{11} + q^{13} - q^{17} - 2q^{19} + O(q^{20})$$

## 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. 