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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5491.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5491.b1 | 5491a3 | \([0, -1, 1, -222337, -40278040]\) | \(-50357871050752/19\) | \(-458613811\) | \([]\) | \(15120\) | \(1.4500\) | |
5491.b2 | 5491a2 | \([0, -1, 1, -2697, -56465]\) | \(-89915392/6859\) | \(-165559585771\) | \([]\) | \(5040\) | \(0.90074\) | |
5491.b3 | 5491a1 | \([0, -1, 1, 193, -110]\) | \(32768/19\) | \(-458613811\) | \([]\) | \(1680\) | \(0.35143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5491.b have rank \(0\).
Complex multiplication
The elliptic curves in class 5491.b do not have complex multiplication.Modular form 5491.2.a.b
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.