# Properties

 Label 15680.x Number of curves $2$ Conductor $15680$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.x1 15680ds2 $$[0, 1, 0, -47105, 2782975]$$ $$2185454/625$$ $$3305767485440000$$ $$[2]$$ $$86016$$ $$1.6844$$
15680.x2 15680ds1 $$[0, 1, 0, 7775, 291423]$$ $$19652/25$$ $$-66115349708800$$ $$[2]$$ $$43008$$ $$1.3379$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.x

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + q^{9} + 4q^{11} + 2q^{13} - 2q^{15} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.