# Properties

 Label 176505.r Number of curves 4 Conductor 176505 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176505.r1")

sage: E.isogeny_class()

## Elliptic curves in class 176505.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176505.r1 176505s4 [1, 1, 0, -189147, -31739316]  1105920
176505.r2 176505s2 [1, 1, 0, -12642, -427329] [2, 2] 552960
176505.r3 176505s1 [1, 1, 0, -4237, 98824]  276480 $$\Gamma_0(N)$$-optimal
176505.r4 176505s3 [1, 1, 0, 29383, -2621034]  1105920

## Rank

sage: E.rank()

The elliptic curves in class 176505.r have rank $$0$$.

## Modular form 176505.2.a.r

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{7} - 3q^{8} + q^{9} + q^{10} + q^{12} + 6q^{13} - q^{14} - q^{15} - q^{16} - 2q^{17} + q^{18} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 