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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 122694ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122694.n2 | 122694ba1 | \([1, 1, 0, -11768825, -54245223963]\) | \(-9595703125/62099136\) | \(-1166626506051578947497408\) | \([2]\) | \(13478400\) | \(3.3015\) | \(\Gamma_0(N)\)-optimal |
122694.n1 | 122694ba2 | \([1, 1, 0, -298872785, -1984674830211]\) | \(157158018407125/382657176\) | \(7188795738678942495921528\) | \([2]\) | \(26956800\) | \(3.6481\) |
Rank
sage: E.rank()
The elliptic curves in class 122694ba have rank \(1\).
Complex multiplication
The elliptic curves in class 122694ba do not have complex multiplication.Modular form 122694.2.a.ba
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.