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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 19950.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19950.ba1 | 19950ba2 | \([1, 0, 1, -117723896, 491270148038]\) | \(1443469370754216095414793773/1214743716234132166656\) | \(151842964529266520832000\) | \([2]\) | \(4257792\) | \(3.3757\) | |
19950.ba2 | 19950ba1 | \([1, 0, 1, -5749496, 11123920838]\) | \(-168152341439816283534893/330377478011967504384\) | \(-41297184751495938048000\) | \([2]\) | \(2128896\) | \(3.0291\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19950.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 19950.ba do not have complex multiplication.Modular form 19950.2.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 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.