Properties

Label 6498.t
Number of curves $4$
Conductor $6498$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 6498.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6498.t1 6498v3 \([1, -1, 1, -1390640, -630851601]\) \(8671983378625/82308\) \(2822871980170692\) \([2]\) \(103680\) \(2.1270\)  
6498.t2 6498v4 \([1, -1, 1, -1358150, -661756089]\) \(-8078253774625/846825858\) \(-29043118367986164642\) \([2]\) \(207360\) \(2.4736\)  
6498.t3 6498v1 \([1, -1, 1, -26060, 130191]\) \(57066625/32832\) \(1126020956079168\) \([2]\) \(34560\) \(1.5777\) \(\Gamma_0(N)\)-optimal
6498.t4 6498v2 \([1, -1, 1, 103900, 961935]\) \(3616805375/2105352\) \(-72206093808576648\) \([2]\) \(69120\) \(1.9243\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6498.t have rank \(0\).

Complex multiplication

The elliptic curves in class 6498.t do not have complex multiplication.

Modular form 6498.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{7} + q^{8} + 4 q^{13} - 4 q^{14} + q^{16} - 6 q^{17} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.