# Properties

 Label 15680.br Number of curves $2$ Conductor $15680$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.br1 15680dp2 $$[0, -1, 0, -157845, -24085235]$$ $$-225637236736/1715$$ $$-3305767485440$$ $$[]$$ $$55296$$ $$1.5771$$
15680.br2 15680dp1 $$[0, -1, 0, -1045, -63475]$$ $$-65536/875$$ $$-1686616064000$$ $$[]$$ $$18432$$ $$1.0278$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15680.br have rank $$0$$.

## Complex multiplication

The elliptic curves in class 15680.br do not have complex multiplication.

## Modular form 15680.2.a.br

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 2q^{9} + 3q^{11} - q^{13} - q^{15} + 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 