Properties

Label 11466.z
Number of curves $4$
Conductor $11466$
CM no
Rank $0$
Graph

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

Elliptic curves in class 11466.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11466.z1 11466y3 \([1, -1, 0, -183906, 30401230]\) \(8020417344913/187278\) \(16062107608638\) \([2]\) \(73728\) \(1.6462\)  
11466.z2 11466y2 \([1, -1, 0, -11916, 440572]\) \(2181825073/298116\) \(25568252928036\) \([2, 2]\) \(36864\) \(1.2997\)  
11466.z3 11466y1 \([1, -1, 0, -3096, -58640]\) \(38272753/4368\) \(374626416528\) \([2]\) \(18432\) \(0.95309\) \(\Gamma_0(N)\)-optimal
11466.z4 11466y4 \([1, -1, 0, 18954, 2323642]\) \(8780064047/32388174\) \(-2777808050253054\) \([2]\) \(73728\) \(1.6462\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11466.z have rank \(0\).

Complex multiplication

The elliptic curves in class 11466.z do not have complex multiplication.

Modular form 11466.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} - q^{8} - 2 q^{10} + 4 q^{11} + q^{13} + q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.