# Properties

 Label 60984z Number of curves $4$ Conductor $60984$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 60984z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.f4 60984z1 $$[0, 0, 0, -7986, 1782209]$$ $$-2725888/64827$$ $$-1339551904421808$$ $$[2]$$ $$276480$$ $$1.5833$$ $$\Gamma_0(N)$$-optimal
60984.f3 60984z2 $$[0, 0, 0, -274791, 55196570]$$ $$6940769488/35721$$ $$11809926994086144$$ $$[2, 2]$$ $$552960$$ $$1.9299$$
60984.f2 60984z3 $$[0, 0, 0, -427251, -12892066]$$ $$6522128932/3720087$$ $$4919678159250742272$$ $$[2]$$ $$1105920$$ $$2.2764$$
60984.f1 60984z4 $$[0, 0, 0, -4391211, 3541804310]$$ $$7080974546692/189$$ $$249945544848384$$ $$[2]$$ $$1105920$$ $$2.2764$$

## Rank

sage: E.rank()

The elliptic curves in class 60984z have rank $$1$$.

## Complex multiplication

The elliptic curves in class 60984z do not have complex multiplication.

## Modular form 60984.2.a.z

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.