Properties

Label 6630.t
Number of curves 4
Conductor 6630
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6630.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6630.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6630.t1 6630s4 [1, 1, 1, -76620, 8117397] [2] 46080  
6630.t2 6630s3 [1, 1, 1, -64220, -6258283] [2] 46080  
6630.t3 6630s2 [1, 1, 1, -6420, 30357] [2, 2] 23040  
6630.t4 6630s1 [1, 1, 1, 1580, 4757] [4] 11520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6630.t have rank \(0\).

Modular form 6630.2.a.t

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 4q^{7} + q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + q^{13} + 4q^{14} - q^{15} + q^{16} - q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

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.