# Properties

 Label 15680.n Number of curves $4$ Conductor $15680$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.n1 15680s3 $$[0, 1, 0, -8101, 277899]$$ $$488095744/125$$ $$15059072000$$ $$$$ $$17280$$ $$0.93888$$
15680.n2 15680s4 $$[0, 1, 0, -7121, 348655]$$ $$-20720464/15625$$ $$-30118144000000$$ $$$$ $$34560$$ $$1.2855$$
15680.n3 15680s1 $$[0, 1, 0, -261, -1205]$$ $$16384/5$$ $$602362880$$ $$$$ $$5760$$ $$0.38958$$ $$\Gamma_0(N)$$-optimal
15680.n4 15680s2 $$[0, 1, 0, 719, -7281]$$ $$21296/25$$ $$-48189030400$$ $$$$ $$11520$$ $$0.73615$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.n

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 