# Properties

 Label 185150f Number of curves $2$ Conductor $185150$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 185150f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.bk2 185150f1 $$[1, 0, 0, 455987, -557455983]$$ $$4533086375/60669952$$ $$-140333285623552000000$$ $$$$ $$8515584$$ $$2.5466$$ $$\Gamma_0(N)$$-optimal
185150.bk1 185150f2 $$[1, 0, 0, -8008013, -8166591983]$$ $$24553362849625/1755162752$$ $$4059798098937602000000$$ $$$$ $$17031168$$ $$2.8932$$

## Rank

sage: E.rank()

The elliptic curves in class 185150f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 185150f do not have complex multiplication.

## Modular form 185150.2.a.f

sage: E.q_eigenform(10)

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