# Properties

 Label 47190i Number of curves $2$ Conductor $47190$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 47190i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.o2 47190i1 $$[1, 1, 0, 163, -1239]$$ $$356400829/760500$$ $$-1012225500$$ $$$$ $$20736$$ $$0.41222$$ $$\Gamma_0(N)$$-optimal
47190.o1 47190i2 $$[1, 1, 0, -1267, -14681]$$ $$169204136291/32906250$$ $$43798218750$$ $$$$ $$41472$$ $$0.75880$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47190.2.a.i

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 