# Properties

 Label 60984.q Number of curves $2$ Conductor $60984$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.q1 60984cb2 $$[0, 0, 0, -3531, -67034]$$ $$2450086/441$$ $$876343007232$$ $$[2]$$ $$61440$$ $$1.0106$$
60984.q2 60984cb1 $$[0, 0, 0, 429, -6050]$$ $$8788/21$$ $$-20865309696$$ $$[2]$$ $$30720$$ $$0.66406$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 60984.q have rank $$0$$.

## Complex multiplication

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

## Modular form 60984.2.a.q

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.