# Properties

 Label 235200g Number of curves 2 Conductor 235200 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.g1")

sage: E.isogeny_class()

## Elliptic curves in class 235200g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.g1 235200g1 [0, -1, 0, -56513, 5024097]  1179648 $$\Gamma_0(N)$$-optimal
235200.g2 235200g2 [0, -1, 0, 21887, 17803297]  2359296

## Rank

sage: E.rank()

The elliptic curves in class 235200g have rank $$2$$.

## Modular form 235200.2.a.g

sage: E.q_eigenform(10)

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

## 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. 