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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)
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.