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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 2142t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2142.l2 | 2142t1 | \([1, -1, 1, 283, 285]\) | \(3449795831/2071552\) | \(-1510161408\) | \([2]\) | \(1920\) | \(0.45057\) | \(\Gamma_0(N)\)-optimal |
2142.l1 | 2142t2 | \([1, -1, 1, -1157, 3165]\) | \(234770924809/130960928\) | \(95470516512\) | \([2]\) | \(3840\) | \(0.79714\) |
Rank
sage: E.rank()
The elliptic curves in class 2142t have rank \(1\).
Complex multiplication
The elliptic curves in class 2142t 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 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.