# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.r1 15680v2 $$[0, 1, 0, -3735041, -2779534241]$$ $$544737993463/20000$$ $$211569119068160000$$ $$$$ $$430080$$ $$2.4121$$
15680.r2 15680v1 $$[0, 1, 0, -222721, -47651745]$$ $$-115501303/25600$$ $$-270808472407244800$$ $$$$ $$215040$$ $$2.0655$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.r

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} + q^{9} + 4q^{11} - 2q^{13} + 2q^{15} + 8q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 