# Properties

 Label 960.k Number of curves $4$ Conductor $960$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 960.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.k1 960f3 $$[0, 1, 0, -641, -6465]$$ $$890277128/15$$ $$491520$$ $$$$ $$256$$ $$0.22238$$
960.k2 960f4 $$[0, 1, 0, -161, 639]$$ $$14172488/1875$$ $$61440000$$ $$$$ $$256$$ $$0.22238$$
960.k3 960f2 $$[0, 1, 0, -41, -105]$$ $$1906624/225$$ $$921600$$ $$[2, 2]$$ $$128$$ $$-0.12420$$
960.k4 960f1 $$[0, 1, 0, 4, -6]$$ $$85184/405$$ $$-25920$$ $$$$ $$64$$ $$-0.47077$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 960.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 960.k do not have complex multiplication.

## Modular form960.2.a.k

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 