# Properties

 Label 60984.s Number of curves $4$ Conductor $60984$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.s1 60984bh4 $$[0, 0, 0, -165891, 25973134]$$ $$381775972/567$$ $$749836634545152$$ $$$$ $$368640$$ $$1.7552$$
60984.s2 60984bh2 $$[0, 0, 0, -13431, 146410]$$ $$810448/441$$ $$145801567828224$$ $$[2, 2]$$ $$184320$$ $$1.4086$$
60984.s3 60984bh1 $$[0, 0, 0, -7986, -272855]$$ $$2725888/21$$ $$433933237584$$ $$$$ $$92160$$ $$1.0621$$ $$\Gamma_0(N)$$-optimal
60984.s4 60984bh3 $$[0, 0, 0, 51909, 1152646]$$ $$11696828/7203$$ $$-9525702431443968$$ $$$$ $$368640$$ $$1.7552$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 60984.2.a.s

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 