# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dr1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.dr1 15680ba1 $$[0, 0, 0, -8428, -297808]$$ $$-5154200289/20$$ $$-256901120$$ $$[]$$ $$23040$$ $$0.82690$$ $$\Gamma_0(N)$$-optimal
15680.dr2 15680ba2 $$[0, 0, 0, 58772, 2825648]$$ $$1747829720511/1280000000$$ $$-16441671680000000$$ $$[]$$ $$161280$$ $$1.7999$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.dr

sage: E.q_eigenform(10)

$$q + 3q^{3} - q^{5} + 6q^{9} + 2q^{11} - 3q^{15} + 4q^{17} - 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.