# Properties

 Label 177450.hz Number of curves $2$ Conductor $177450$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hz1")

sage: E.isogeny_class()

## Elliptic curves in class 177450.hz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.hz1 177450l2 $$[1, 0, 0, -59238, -5876508]$$ $$-7620530425/526848$$ $$-1589371667520000$$ $$[]$$ $$1516320$$ $$1.6678$$
177450.hz2 177450l1 $$[1, 0, 0, 4137, -7983]$$ $$2595575/1512$$ $$-4561334505000$$ $$[]$$ $$505440$$ $$1.1185$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 177450.hz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 177450.hz do not have complex multiplication.

## Modular form 177450.2.a.hz

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 6q^{11} + q^{12} - q^{14} + q^{16} + 3q^{17} + q^{18} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 