# Properties

 Label 177450iq Number of curves $2$ Conductor $177450$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("iq1")

sage: E.isogeny_class()

## Elliptic curves in class 177450iq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bm2 177450iq1 $$[1, 1, 0, 103425, -997875]$$ $$2595575/1512$$ $$-71270851640625000$$ $$[]$$ $$2527200$$ $$1.9232$$ $$\Gamma_0(N)$$-optimal
177450.bm1 177450iq2 $$[1, 1, 0, -1480950, -734563500]$$ $$-7620530425/526848$$ $$-24833932305000000000$$ $$[]$$ $$7581600$$ $$2.4725$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 177450.2.a.iq

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 Cremona 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 Cremona labels.