# Properties

 Label 119952.f Number of curves $2$ Conductor $119952$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 119952.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.f1 119952fs2 $$[0, 0, 0, -2686719, 1694515354]$$ $$40685771728/14739$$ $$776990864553732864$$ $$[]$$ $$3773952$$ $$2.4015$$
119952.f2 119952fs1 $$[0, 0, 0, -93639, -8100974]$$ $$1722448/459$$ $$24196947339043584$$ $$[]$$ $$1257984$$ $$1.8521$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 119952.f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 119952.f do not have complex multiplication.

## Modular form 119952.2.a.f

sage: E.q_eigenform(10)

$$q - 3q^{5} - 6q^{11} - 5q^{13} - q^{17} + 2q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 