# Properties

 Label 960o Number of curves $8$ Conductor $960$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 960o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.p8 960o1 $$[0, 1, 0, 95, -1057]$$ $$357911/2160$$ $$-566231040$$ $$[2]$$ $$384$$ $$0.36143$$ $$\Gamma_0(N)$$-optimal
960.p6 960o2 $$[0, 1, 0, -1185, -14625]$$ $$702595369/72900$$ $$19110297600$$ $$[2, 2]$$ $$768$$ $$0.70801$$
960.p7 960o3 $$[0, 1, 0, -865, 31775]$$ $$-273359449/1536000$$ $$-402653184000$$ $$[2]$$ $$1152$$ $$0.91074$$
960.p4 960o4 $$[0, 1, 0, -18465, -971937]$$ $$2656166199049/33750$$ $$8847360000$$ $$[2]$$ $$1536$$ $$1.0546$$
960.p5 960o5 $$[0, 1, 0, -4385, 94815]$$ $$35578826569/5314410$$ $$1393140695040$$ $$[4]$$ $$1536$$ $$1.0546$$
960.p3 960o6 $$[0, 1, 0, -21345, 1190943]$$ $$4102915888729/9000000$$ $$2359296000000$$ $$[2, 2]$$ $$2304$$ $$1.2573$$
960.p2 960o7 $$[0, 1, 0, -29025, 249375]$$ $$10316097499609/5859375000$$ $$1536000000000000$$ $$[2]$$ $$4608$$ $$1.6039$$
960.p1 960o8 $$[0, 1, 0, -341345, 76646943]$$ $$16778985534208729/81000$$ $$21233664000$$ $$[4]$$ $$4608$$ $$1.6039$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form960.2.a.o

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.