# Properties

 Label 215950bb Number of curves 2 Conductor 215950 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("215950.o1")

sage: E.isogeny_class()

## Elliptic curves in class 215950bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
215950.o2 215950bb1 [1, -1, 0, -3445792, 2499871616] [] 20942208 $$\Gamma_0(N)$$-optimal
215950.o1 215950bb2 [1, -1, 0, -31769542, -301546607134] [] 146595456

## Rank

sage: E.rank()

The elliptic curves in class 215950bb have rank $$1$$.

## Modular form 215950.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} + 3q^{3} + q^{4} - 3q^{6} - q^{7} - q^{8} + 6q^{9} - 2q^{11} + 3q^{12} + 7q^{13} + q^{14} + q^{16} - 4q^{17} - 6q^{18} - q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 