Properties

Label 20286.z
Number of curves $4$
Conductor $20286$
CM no
Rank $0$
Graph

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

Elliptic curves in class 20286.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.z1 20286bd4 \([1, -1, 0, -108936, 13864122]\) \(1666957239793/301806\) \(25884729914526\) \([2]\) \(98304\) \(1.5773\)  
20286.z2 20286bd3 \([1, -1, 0, -47196, -3805866]\) \(135559106353/5037138\) \(432015787201698\) \([2]\) \(98304\) \(1.5773\)  
20286.z3 20286bd2 \([1, -1, 0, -7506, 171072]\) \(545338513/171396\) \(14699970074916\) \([2, 2]\) \(49152\) \(1.2307\)  
20286.z4 20286bd1 \([1, -1, 0, 1314, 17604]\) \(2924207/3312\) \(-284057392752\) \([2]\) \(24576\) \(0.88413\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20286.z have rank \(0\).

Complex multiplication

The elliptic curves in class 20286.z do not have complex multiplication.

Modular form 20286.2.a.z

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