# Properties

 Label 115920.bj Number of curves $2$ Conductor $115920$ CM no Rank $2$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.bj1 115920bb2 $$[0, 0, 0, -10083, 386818]$$ $$75933869762/648025$$ $$967496140800$$ $$[2]$$ $$221184$$ $$1.1247$$
115920.bj2 115920bb1 $$[0, 0, 0, -1083, -3782]$$ $$188183524/100625$$ $$75116160000$$ $$[2]$$ $$110592$$ $$0.77813$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 115920.bj have rank $$2$$.

## Complex multiplication

The elliptic curves in class 115920.bj do not have complex multiplication.

## Modular form 115920.2.a.bj

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} - 2q^{11} - 4q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.