Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.f4 60984z1 \([0, 0, 0, -7986, 1782209]\) \(-2725888/64827\) \(-1339551904421808\) \([2]\) \(276480\) \(1.5833\) \(\Gamma_0(N)\)-optimal
60984.f3 60984z2 \([0, 0, 0, -274791, 55196570]\) \(6940769488/35721\) \(11809926994086144\) \([2, 2]\) \(552960\) \(1.9299\)  
60984.f2 60984z3 \([0, 0, 0, -427251, -12892066]\) \(6522128932/3720087\) \(4919678159250742272\) \([2]\) \(1105920\) \(2.2764\)  
60984.f1 60984z4 \([0, 0, 0, -4391211, 3541804310]\) \(7080974546692/189\) \(249945544848384\) \([2]\) \(1105920\) \(2.2764\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 60984.2.a.z

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