# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.m1 60984y4 $$[0, 0, 0, -697213011, -5024378661874]$$ $$14171198121996897746/4077720290568771$$ $$10785270050428806222225610752$$ $$[2]$$ $$44236800$$ $$4.0854$$
60984.m2 60984y2 $$[0, 0, 0, -639234651, -6219927232090]$$ $$21843440425782779332/3100814593569$$ $$4100713190811767696753664$$ $$[2, 2]$$ $$22118400$$ $$3.7388$$
60984.m3 60984y1 $$[0, 0, 0, -639212871, -6220372323814]$$ $$87364831012240243408/1760913$$ $$582185660338098432$$ $$[2]$$ $$11059200$$ $$3.3922$$ $$\Gamma_0(N)$$-optimal
60984.m4 60984y3 $$[0, 0, 0, -581604771, -7386989931970]$$ $$-8226100326647904626/4152140742401883$$ $$-10982106668220235816520964096$$ $$[2]$$ $$44236800$$ $$4.0854$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 60984.2.a.m

sage: E.q_eigenform(10)

$$q - 2 q^{5} - q^{7} + 6 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})$$

## 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 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.