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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 9338.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9338.e1 | 9338b2 | \([1, 1, 0, -173111141, 876596829545]\) | \(573718392227901342193352375257/22016176259779893044\) | \(22016176259779893044\) | \([2]\) | \(1455104\) | \(3.2025\) | |
9338.e2 | 9338b1 | \([1, 1, 0, -10803361, 13736209509]\) | \(-139444195316122186685933977/867810592237096964848\) | \(-867810592237096964848\) | \([2]\) | \(727552\) | \(2.8560\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9338.e have rank \(0\).
Complex multiplication
The elliptic curves in class 9338.e do not have complex multiplication.Modular form 9338.2.a.e
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.