# Properties

 Label 47190b Number of curves $2$ Conductor $47190$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 47190b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.f2 47190b1 $$[1, 1, 0, -220948, 40423552]$$ $$-673350049820449/10617750000$$ $$-18809991807750000$$ $$$$ $$552960$$ $$1.9241$$ $$\Gamma_0(N)$$-optimal
47190.f1 47190b2 $$[1, 1, 0, -3548448, 2571320052]$$ $$2789222297765780449/677605500$$ $$1200419477185500$$ $$$$ $$1105920$$ $$2.2707$$

## Rank

sage: E.rank()

The elliptic curves in class 47190b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 47190b do not have complex multiplication.

## Modular form 47190.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - q^{13} - 2q^{14} + q^{15} + q^{16} + 2q^{17} - q^{18} + O(q^{20})$$ ## 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. 