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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 72128.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.be1 | 72128a2 | \([0, 0, 0, -191884, -32351760]\) | \(50668941906/1127\) | \(17378891923456\) | \([2]\) | \(196608\) | \(1.6555\) | |
72128.be2 | 72128a1 | \([0, 0, 0, -11564, -543312]\) | \(-22180932/3703\) | \(-28551036731392\) | \([2]\) | \(98304\) | \(1.3089\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.be have rank \(0\).
Complex multiplication
The elliptic curves in class 72128.be do not have complex multiplication.Modular form 72128.2.a.be
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.