# Properties

 Label 179520ht Number of curves 2 Conductor 179520 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("179520.p1")

sage: E.isogeny_class()

## Elliptic curves in class 179520ht

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.p2 179520ht1 [0, -1, 0, -56321, 2284545]  1032192 $$\Gamma_0(N)$$-optimal
179520.p1 179520ht2 [0, -1, 0, -752641, 251427841]  2064384

## Rank

sage: E.rank()

The elliptic curves in class 179520ht have rank $$1$$.

## Modular form 179520.2.a.p

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 Cremona 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 Cremona labels. 