# Properties

 Label 230115y Number of curves 2 Conductor 230115 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("230115.y1")

sage: E.isogeny_class()

## Elliptic curves in class 230115y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
230115.y1 230115y1 [1, 0, 1, -197593, -33820969]  912384 $$\Gamma_0(N)$$-optimal
230115.y2 230115y2 [1, 0, 1, -184368, -38539649]  1824768

## Rank

sage: E.rank()

The elliptic curves in class 230115y have rank $$1$$.

## Modular form 230115.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3q^{8} + q^{9} + q^{10} - 2q^{11} - q^{12} + 2q^{13} + q^{15} - q^{16} + 4q^{17} + q^{18} + O(q^{20})$$

## 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. 