# Properties

 Label 17850bp Number of curves $2$ Conductor $17850$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bp1")

sage: E.isogeny_class()

## Elliptic curves in class 17850bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17850.bt2 17850bp1 $$[1, 0, 0, 2037, 42417]$$ $$59822347031/83966400$$ $$-1311975000000$$ $$[2]$$ $$27648$$ $$1.0108$$ $$\Gamma_0(N)$$-optimal
17850.bt1 17850bp2 $$[1, 0, 0, -12963, 417417]$$ $$15417797707369/4080067320$$ $$63751051875000$$ $$[2]$$ $$55296$$ $$1.3574$$

## Rank

sage: E.rank()

The elliptic curves in class 17850bp have rank $$1$$.

## Complex multiplication

The elliptic curves in class 17850bp do not have complex multiplication.

## Modular form 17850.2.a.bp

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} + 2q^{13} - q^{14} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.