# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bz1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bz1 119952l2 $$[0, 0, 0, -254751, 48942670]$$ $$2248430329584/28647703$$ $$23296022394027264$$ $$$$ $$1032192$$ $$1.9494$$
119952.bz2 119952l1 $$[0, 0, 0, -2646, 2000719]$$ $$-40310784/34000561$$ $$-1728057024470448$$ $$$$ $$516096$$ $$1.6028$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 119952.2.a.bz

sage: E.q_eigenform(10)

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