# Properties

 Label 179088bh Number of curves 2 Conductor 179088 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("179088.n1")

sage: E.isogeny_class()

## Elliptic curves in class 179088bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179088.n1 179088bh1 [0, -1, 0, -2492896, -1514524928] [] 3161088 $$\Gamma_0(N)$$-optimal
179088.n2 179088bh2 [0, -1, 0, 13833344, 66885734272] [] 22127616

## Rank

sage: E.rank()

The elliptic curves in class 179088bh have rank $$0$$.

## Modular form 179088.2.a.n

sage: E.q_eigenform(10)

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

## 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 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.