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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 43350.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43350.ba1 | 43350bj2 | \([1, 0, 1, -3253101, -2258637152]\) | \(-843137281012581793/216\) | \(-975375000\) | \([]\) | \(734832\) | \(2.0073\) | |
43350.ba2 | 43350bj1 | \([1, 0, 1, -40101, -3111152]\) | \(-1579268174113/10077696\) | \(-45507096000000\) | \([]\) | \(244944\) | \(1.4580\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43350.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 43350.ba do not have complex multiplication.Modular form 43350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.