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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 2112.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2112.t1 | 2112q2 | \([0, 1, 0, -5169, 141327]\) | \(932410994128/29403\) | \(481738752\) | \([2]\) | \(1920\) | \(0.76194\) | |
2112.t2 | 2112q1 | \([0, 1, 0, -309, 2331]\) | \(-3196715008/649539\) | \(-665127936\) | \([2]\) | \(960\) | \(0.41536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2112.t have rank \(1\).
Complex multiplication
The elliptic curves in class 2112.t do not have complex multiplication.Modular form 2112.2.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.