# Properties

 Label 960.f Number of curves $4$ Conductor $960$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 960.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.f1 960k3 $$[0, -1, 0, -225, -1215]$$ $$38614472/405$$ $$13271040$$ $$$$ $$256$$ $$0.18331$$
960.f2 960k2 $$[0, -1, 0, -25, 25]$$ $$438976/225$$ $$921600$$ $$[2, 2]$$ $$128$$ $$-0.16327$$
960.f3 960k1 $$[0, -1, 0, -20, 42]$$ $$14526784/15$$ $$960$$ $$$$ $$64$$ $$-0.50984$$ $$\Gamma_0(N)$$-optimal
960.f4 960k4 $$[0, -1, 0, 95, 97]$$ $$2863288/1875$$ $$-61440000$$ $$$$ $$256$$ $$0.18331$$

## Rank

sage: E.rank()

The elliptic curves in class 960.f have rank $$1$$.

## Complex multiplication

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

## Modular form960.2.a.f

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 