Properties

Label 60984f
Number of curves $2$
Conductor $60984$
CM no
Rank $2$
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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 \([0, 0, 0, -64251, 6263686]\) \(598885164/539\) \(26400283886592\) \([2]\) \(215040\) \(1.4998\) \(\Gamma_0(N)\)-optimal
60984.g2 60984f2 \([0, 0, 0, -49731, 9170590]\) \(-138853062/290521\) \(-28459506029746176\) \([2]\) \(430080\) \(1.8463\)  

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