# Properties

 Label 119952.fi Number of curves $4$ Conductor $119952$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("fi1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fi1 119952x4 $$[0, 0, 0, -966819, 365834882]$$ $$569001644066/122451$$ $$21508397634705408$$ $$[2]$$ $$1179648$$ $$2.1287$$
119952.fi2 119952x3 $$[0, 0, 0, -437619, -108180142]$$ $$52767497666/1753941$$ $$308078010435299328$$ $$[2]$$ $$1179648$$ $$2.1287$$
119952.fi3 119952x2 $$[0, 0, 0, -67179, 4359530]$$ $$381775972/127449$$ $$11193145707856896$$ $$[2, 2]$$ $$589824$$ $$1.7821$$
119952.fi4 119952x1 $$[0, 0, 0, 12201, 469910]$$ $$9148592/9639$$ $$-211635107921664$$ $$[2]$$ $$294912$$ $$1.4355$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 119952.fi have rank $$1$$.

## Complex multiplication

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

## Modular form 119952.2.a.fi

sage: E.q_eigenform(10)

$$q + 2q^{5} - 4q^{11} - 2q^{13} - q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.