# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 960.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.n1 960p4 $$[0, 1, 0, -865, 9503]$$ $$546718898/405$$ $$53084160$$ $$$$ $$512$$ $$0.41598$$
960.n2 960p3 $$[0, 1, 0, -545, -5025]$$ $$136835858/1875$$ $$245760000$$ $$$$ $$512$$ $$0.41598$$
960.n3 960p2 $$[0, 1, 0, -65, 63]$$ $$470596/225$$ $$14745600$$ $$[2, 2]$$ $$256$$ $$0.069403$$
960.n4 960p1 $$[0, 1, 0, 15, 15]$$ $$21296/15$$ $$-245760$$ $$$$ $$128$$ $$-0.27717$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form960.2.a.n

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4 q^{7} + q^{9} + 6 q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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. 