Properties

Label 126960.l
Number of curves $6$
Conductor $126960$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 126960.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126960.l1 126960b6 \([0, -1, 0, -1692976, -847296224]\) \(1770025017602/75\) \(22738312550400\) \([2]\) \(1622016\) \(2.0477\)  
126960.l2 126960b4 \([0, -1, 0, -105976, -13169024]\) \(868327204/5625\) \(852686720640000\) \([2, 2]\) \(811008\) \(1.7012\)  
126960.l3 126960b5 \([0, -1, 0, -42496, -28861280]\) \(-27995042/1171875\) \(-355286133600000000\) \([2]\) \(1622016\) \(2.0477\)  
126960.l4 126960b2 \([0, -1, 0, -10756, 85600]\) \(3631696/2025\) \(76741804857600\) \([2, 2]\) \(405504\) \(1.3546\)  
126960.l5 126960b1 \([0, -1, 0, -8111, 283446]\) \(24918016/45\) \(106585840080\) \([2]\) \(202752\) \(1.0080\) \(\Gamma_0(N)\)-optimal
126960.l6 126960b3 \([0, -1, 0, 42144, 635760]\) \(54607676/32805\) \(-4972868954772480\) \([2]\) \(811008\) \(1.7012\)  

Rank

sage: E.rank()
 

The elliptic curves in class 126960.l have rank \(0\).

Complex multiplication

The elliptic curves in class 126960.l do not have complex multiplication.

Modular form 126960.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 4 q^{11} + 6 q^{13} + q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.