# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 47190f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.b2 47190f1 $$[1, 1, 0, -121936663, 519239706517]$$ $$-113180217375258301213009/260161419375000000$$ $$-460891824269394375000000$$ $$$$ $$9676800$$ $$3.4219$$ $$\Gamma_0(N)$$-optimal
47190.b1 47190f2 $$[1, 1, 0, -1952061663, 33195389531517]$$ $$464352938845529653759213009/2445173327025000$$ $$4331773704397736025000$$ $$$$ $$19353600$$ $$3.7684$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47190.2.a.f

sage: E.q_eigenform(10)

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