# Properties

 Label 119952.fv Number of curves $2$ Conductor $119952$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("fv1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.fv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fv1 119952dd2 $$[0, 0, 0, -7531839, -7530582150]$$ $$79708988544624/4802079233$$ $$2846746657491138614016$$ $$[2]$$ $$6082560$$ $$2.8692$$
119952.fv2 119952dd1 $$[0, 0, 0, -7419384, -7778545425]$$ $$1219067475001344/4857223$$ $$179964795834136656$$ $$[2]$$ $$3041280$$ $$2.5227$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 119952.2.a.fv

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{11} + 6q^{13} + q^{17} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.