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Properties

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

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

Elliptic curves in class 6630.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6630.t1 6630s4 \([1, 1, 1, -76620, 8117397]\) \(49745123032831462081/97939634471640\) \(97939634471640\) \([2]\) \(46080\) \(1.5727\)  
6630.t2 6630s3 \([1, 1, 1, -64220, -6258283]\) \(29291056630578924481/175463302795560\) \(175463302795560\) \([2]\) \(46080\) \(1.5727\)  
6630.t3 6630s2 \([1, 1, 1, -6420, 30357]\) \(29263955267177281/16463793153600\) \(16463793153600\) \([2, 2]\) \(23040\) \(1.2261\)  
6630.t4 6630s1 \([1, 1, 1, 1580, 4757]\) \(436192097814719/259683840000\) \(-259683840000\) \([4]\) \(11520\) \(0.87955\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 6630.t do not have complex multiplication.

Modular form 6630.2.a.t

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.