# Properties

 Label 47190.a Number of curves $2$ Conductor $47190$ CM no Rank $1$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 47190.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.a1 47190g2 $$[1, 1, 0, -5568, 140958]$$ $$10779215329/1232010$$ $$2182580867610$$ $$$$ $$122880$$ $$1.0999$$
47190.a2 47190g1 $$[1, 1, 0, 482, 11488]$$ $$6967871/35100$$ $$-62181791100$$ $$$$ $$61440$$ $$0.75333$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 47190.a have rank $$1$$.

## Complex multiplication

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

## Modular form 47190.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 2q^{7} - q^{8} + q^{9} + q^{10} - q^{12} + q^{13} + 2q^{14} + q^{15} + q^{16} - 8q^{17} - q^{18} + 6q^{19} + O(q^{20})$$ ## 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 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. 