# Properties

 Label 133952.bi Number of curves $2$ Conductor $133952$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 133952.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
133952.bi1 133952q2 $$[0, 0, 0, -1340, -1584]$$ $$16241202000/9332687$$ $$152906743808$$ $$$$ $$92160$$ $$0.83572$$
133952.bi2 133952q1 $$[0, 0, 0, -880, 10008]$$ $$73598976000/336973$$ $$345060352$$ $$$$ $$46080$$ $$0.48914$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 133952.bi have rank $$1$$.

## Complex multiplication

The elliptic curves in class 133952.bi do not have complex multiplication.

## Modular form 133952.2.a.bi

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{9} + q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 