# Properties

 Label 291018.bi Number of curves 2 Conductor 291018 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("291018.bi1")

sage: E.isogeny_class()

## Elliptic curves in class 291018.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
291018.bi1 291018bi1 [1, 0, 1, -26331218, 52017132260] [] 22127616 $$\Gamma_0(N)$$-optimal
291018.bi2 291018bi2 [1, 0, 1, 146114692, -2296207961500] [] 154893312

## Rank

sage: E.rank()

The elliptic curves in class 291018.bi have rank $$1$$.

## Modular form 291018.2.a.bi

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} + q^{14} + q^{15} + q^{16} + 4q^{17} - q^{18} + 8q^{19} + O(q^{20})$$

## 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. 