# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 15680u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.m2 15680u1 [0, 1, 0, -3201, 2618335] [] 80640 $$\Gamma_0(N)$$-optimal
15680.m1 15680u2 [0, 1, 0, -1539841, 734980959] [] 241920

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.u

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} + q^{9} - 3q^{11} + 5q^{13} + 2q^{15} - 6q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.