# Properties

 Label 60984f Number of curves $2$ Conductor $60984$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 60984f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.g1 60984f1 $$[0, 0, 0, -64251, 6263686]$$ $$598885164/539$$ $$26400283886592$$ $$$$ $$215040$$ $$1.4998$$ $$\Gamma_0(N)$$-optimal
60984.g2 60984f2 $$[0, 0, 0, -49731, 9170590]$$ $$-138853062/290521$$ $$-28459506029746176$$ $$$$ $$430080$$ $$1.8463$$

## Rank

sage: E.rank()

The elliptic curves in class 60984f have rank $$2$$.

## Complex multiplication

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

## Modular form 60984.2.a.f

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 