# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cd1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.cd1 15680n1 $$[0, 1, 0, -195281, -33300625]$$ $$-177953104/125$$ $$-578509309952000$$ $$[]$$ $$96768$$ $$1.7689$$ $$\Gamma_0(N)$$-optimal
15680.cd2 15680n2 $$[0, 1, 0, 188879, -141095921]$$ $$161017136/1953125$$ $$-9039207968000000000$$ $$[]$$ $$290304$$ $$2.3182$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.cd

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2q^{9} - 6q^{11} + 2q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.