Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
60984.p1 60984ch4 [0, 0, 0, -325611, 71514630] [2] 327680  
60984.p2 60984ch3 [0, 0, 0, -64251, -4959306] [2] 327680  
60984.p3 60984ch2 [0, 0, 0, -20691, 1078110] [2, 2] 163840  
60984.p4 60984ch1 [0, 0, 0, 1089, 71874] [2] 81920 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 60984.p have rank \(1\).

Complex multiplication

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

Modular form 60984.2.a.p

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{7} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.