# Properties

 Label 380926bi Number of curves $2$ Conductor $380926$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 380926bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
380926.bi2 380926bi1 $$[1, 0, 0, 285522, -276206204]$$ $$4533086375/60669952$$ $$-34452600263603372032$$ $$$$ $$12644352$$ $$2.4296$$ $$\Gamma_0(N)$$-optimal
380926.bi1 380926bi2 $$[1, 0, 0, -5014318, -4046512380]$$ $$24553362849625/1755162752$$ $$996702959188463176832$$ $$$$ $$25288704$$ $$2.7762$$

## Rank

sage: E.rank()

The elliptic curves in class 380926bi have rank $$1$$.

## Complex multiplication

The elliptic curves in class 380926bi do not have complex multiplication.

## Modular form 380926.2.a.bi

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{8} + q^{9} - 4q^{11} - 2q^{12} + q^{16} - 6q^{17} + q^{18} - 6q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 