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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 2142.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2142.t1 | 2142r2 | \([1, -1, 1, -3434, -76575]\) | \(6141556990297/1019592\) | \(743282568\) | \([2]\) | \(1536\) | \(0.71021\) | |
2142.t2 | 2142r1 | \([1, -1, 1, -194, -1407]\) | \(-1102302937/616896\) | \(-449717184\) | \([2]\) | \(768\) | \(0.36364\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2142.t have rank \(0\).
Complex multiplication
The elliptic curves in class 2142.t do not have complex multiplication.Modular form 2142.2.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 LMFDB 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 LMFDB labels.