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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 16800t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16800.br1 | 16800t1 | \([0, 1, 0, -34258, -2452012]\) | \(4446542056384/25725\) | \(25725000000\) | \([2]\) | \(46080\) | \(1.1879\) | \(\Gamma_0(N)\)-optimal |
16800.br2 | 16800t2 | \([0, 1, 0, -33633, -2545137]\) | \(-65743598656/5294205\) | \(-338829120000000\) | \([2]\) | \(92160\) | \(1.5345\) |
Rank
sage: E.rank()
The elliptic curves in class 16800t have rank \(0\).
Complex multiplication
The elliptic curves in class 16800t do not have complex multiplication.Modular form 16800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.