# Properties

 Label 302330.bo Number of curves 2 Conductor 302330 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("302330.bo1")

sage: E.isogeny_class()

## Elliptic curves in class 302330.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
302330.bo1 302330bo2 [1, -1, 1, -62268303, 827481250957] [] 293190912
302330.bo2 302330bo1 [1, -1, 1, -6753753, -6855595463] [] 41884416 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 302330.bo have rank $$0$$.

## Modular form 302330.2.a.bo

sage: E.q_eigenform(10)

$$q + q^{2} + 3q^{3} + q^{4} - q^{5} + 3q^{6} + q^{8} + 6q^{9} - q^{10} - 2q^{11} + 3q^{12} + 7q^{13} - 3q^{15} + q^{16} - 4q^{17} + 6q^{18} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 