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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 10944cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10944.n3 | 10944cb1 | \([0, 0, 0, -876, -8624]\) | \(389017/57\) | \(10892869632\) | \([2]\) | \(6144\) | \(0.65087\) | \(\Gamma_0(N)\)-optimal |
10944.n2 | 10944cb2 | \([0, 0, 0, -3756, 80080]\) | \(30664297/3249\) | \(620893569024\) | \([2, 2]\) | \(12288\) | \(0.99745\) | |
10944.n1 | 10944cb3 | \([0, 0, 0, -58476, 5442640]\) | \(115714886617/1539\) | \(294107480064\) | \([2]\) | \(24576\) | \(1.3440\) | |
10944.n4 | 10944cb4 | \([0, 0, 0, 4884, 394576]\) | \(67419143/390963\) | \(-74714192805888\) | \([2]\) | \(24576\) | \(1.3440\) |
Rank
sage: E.rank()
The elliptic curves in class 10944cb have rank \(1\).
Complex multiplication
The elliptic curves in class 10944cb do not have complex multiplication.Modular form 10944.2.a.cb
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 Cremona 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 Cremona labels.