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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 91728.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91728.b1 | 91728ev2 | \([0, 0, 0, -8967, 284690]\) | \(3631696/507\) | \(11131756376832\) | \([2]\) | \(276480\) | \(1.2297\) | |
91728.b2 | 91728ev1 | \([0, 0, 0, -2352, -39445]\) | \(1048576/117\) | \(160554178512\) | \([2]\) | \(138240\) | \(0.88316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91728.b have rank \(0\).
Complex multiplication
The elliptic curves in class 91728.b do not have complex multiplication.Modular form 91728.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.