Properties

Label 60984.r
Number of curves $2$
Conductor $60984$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.r1 60984bt2 \([0, 0, 0, -13431, -598950]\) \(21882096/7\) \(85715207424\) \([2]\) \(89600\) \(1.0726\)  
60984.r2 60984bt1 \([0, 0, 0, -726, -11979]\) \(-55296/49\) \(-37500403248\) \([2]\) \(44800\) \(0.72608\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 60984.r have rank \(0\).

Complex multiplication

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

Modular form 60984.2.a.r

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.