# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("gp1")

sage: E.isogeny_class()

## Elliptic curves in class 179520.gp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.gp1 179520ep2 [0, 1, 0, -9185, 213375]  393216
179520.gp2 179520ep1 [0, 1, 0, 1695, 24063]  196608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 179520.gp do not have complex multiplication.

## Modular form 179520.2.a.gp

sage: E.q_eigenform(10)

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

## 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. 