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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 164730.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164730.ba1 | 164730cw2 | \([1, 1, 0, -454747, 117463981]\) | \(430864987260889/1601175600\) | \(38648486526116400\) | \([2]\) | \(3538944\) | \(2.0426\) | |
164730.ba2 | 164730cw1 | \([1, 1, 0, -15467, 3514749]\) | \(-16954786009/212094720\) | \(-5119450938535680\) | \([2]\) | \(1769472\) | \(1.6961\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 164730.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 164730.ba do not have complex multiplication.Modular form 164730.2.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.