# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 960.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.b1 960a4 $$[0, -1, 0, -641, 6465]$$ $$890277128/15$$ $$491520$$ $$$$ $$256$$ $$0.22238$$
960.b2 960a3 $$[0, -1, 0, -161, -639]$$ $$14172488/1875$$ $$61440000$$ $$$$ $$256$$ $$0.22238$$
960.b3 960a2 $$[0, -1, 0, -41, 105]$$ $$1906624/225$$ $$921600$$ $$[2, 2]$$ $$128$$ $$-0.12420$$
960.b4 960a1 $$[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.b have rank $$1$$.

## Complex multiplication

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

## Modular form960.2.a.b

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. 