# Properties

 Label 179520.fr Number of curves 2 Conductor 179520 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("179520.fr1")

sage: E.isogeny_class()

## Elliptic curves in class 179520.fr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.fr1 179520bs2 [0, 1, 0, -752641, -251427841]  2064384
179520.fr2 179520bs1 [0, 1, 0, -56321, -2284545]  1032192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 179520.fr have rank $$0$$.

## Modular form 179520.2.a.fr

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 