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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 10626t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10626.t3 | 10626t1 | \([1, 0, 0, -132, 528]\) | \(254478514753/21762048\) | \(21762048\) | \([2]\) | \(3456\) | \(0.14919\) | \(\Gamma_0(N)\)-optimal |
10626.t2 | 10626t2 | \([1, 0, 0, -452, -3120]\) | \(10214075575873/1806590016\) | \(1806590016\) | \([2, 2]\) | \(6912\) | \(0.49577\) | |
10626.t1 | 10626t3 | \([1, 0, 0, -6892, -220792]\) | \(36204575259448513/1527466248\) | \(1527466248\) | \([2]\) | \(13824\) | \(0.84234\) | |
10626.t4 | 10626t4 | \([1, 0, 0, 868, -17640]\) | \(72318867421247/177381135624\) | \(-177381135624\) | \([2]\) | \(13824\) | \(0.84234\) |
Rank
sage: E.rank()
The elliptic curves in class 10626t have rank \(0\).
Complex multiplication
The elliptic curves in class 10626t do not have complex multiplication.Modular form 10626.2.a.t
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.