# Properties

 Label 119952.bi Number of curves $2$ Conductor $119952$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bi1 119952gu2 $$[0, 0, 0, -1961211, 1046700074]$$ $$814544990575471/9268826496$$ $$9493062692230397952$$ $$$$ $$3096576$$ $$2.4547$$
119952.bi2 119952gu1 $$[0, 0, 0, -25851, 41474090]$$ $$-1865409391/724451328$$ $$-741977625446055936$$ $$$$ $$1548288$$ $$2.1082$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 119952.2.a.bi

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 