Properties

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

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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)
 
\(q - 2 q^{5} - q^{7} + 6 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\)  Toggle raw display

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.