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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 209484t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209484.bc2 | 209484t1 | \([0, 0, 0, -444360, -110731867]\) | \(5619712000/184437\) | \(318465635906726352\) | \([2]\) | \(2433024\) | \(2.1319\) | \(\Gamma_0(N)\)-optimal |
209484.bc1 | 209484t2 | \([0, 0, 0, -1087095, 282493406]\) | \(5142706000/1728243\) | \(47746255338904750848\) | \([2]\) | \(4866048\) | \(2.4785\) |
Rank
sage: E.rank()
The elliptic curves in class 209484t have rank \(1\).
Complex multiplication
The elliptic curves in class 209484t do not have complex multiplication.Modular form 209484.2.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.