# Properties

 Label 265200r Number of curves 2 Conductor 265200 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.r1")

sage: E.isogeny_class()

## Elliptic curves in class 265200r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.r1 265200r1 [0, -1, 0, -2442508, 1426112512]  8847360 $$\Gamma_0(N)$$-optimal
265200.r2 265200r2 [0, -1, 0, 837992, 4969052512]  17694720

## Rank

sage: E.rank()

The elliptic curves in class 265200r have rank $$1$$.

## Modular form 265200.2.a.r

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} - 4q^{11} - q^{13} - q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 