# Properties

 Label 72128f Number of curves $2$ Conductor $72128$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 72128f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72128.bv2 72128f1 $$[0, -1, 0, 108127, -64410079]$$ $$4533086375/60669952$$ $$-1871120743228506112$$ $$$$ $$1032192$$ $$2.1869$$ $$\Gamma_0(N)$$-optimal
72128.bv1 72128f2 $$[0, -1, 0, -1898913, -942289375]$$ $$24553362849625/1755162752$$ $$54130938376368422912$$ $$$$ $$2064384$$ $$2.5334$$

## Rank

sage: E.rank()

The elliptic curves in class 72128f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 72128f do not have complex multiplication.

## Modular form 72128.2.a.f

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{9} - 4q^{11} - 6q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 