# Properties

 Label 115920.bm Number of curves $2$ Conductor $115920$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.bm1 115920dk2 $$[0, 0, 0, -33123, 2282978]$$ $$1345938541921/24850350$$ $$74202747494400$$ $$$$ $$294912$$ $$1.4560$$
115920.bm2 115920dk1 $$[0, 0, 0, -3, 103682]$$ $$-1/1555260$$ $$-4643981475840$$ $$$$ $$147456$$ $$1.1094$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.bm

sage: E.q_eigenform(10)

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