# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 47190bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.t2 47190bd1 $$[1, 0, 1, 10263701, -18127813684]$$ $$557820238477845431/985142146218750$$ $$-211173968089389631218750$$ $$$$ $$8553600$$ $$3.1604$$ $$\Gamma_0(N)$$-optimal
47190.t1 47190bd2 $$[1, 0, 1, -347129764, -2498968244038]$$ $$-21580315425730848803929/96405029296875000$$ $$-20665274202850341796875000$$ $$[]$$ $$25660800$$ $$3.7097$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47190.2.a.bd

sage: E.q_eigenform(10)

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