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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 248430.ej
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
248430.ej1 | 248430ej1 | \([1, 0, 1, -124388, 6442958]\) | \(1092727/540\) | \(105180742863034020\) | \([2]\) | \(3096576\) | \(1.9593\) | \(\Gamma_0(N)\)-optimal |
248430.ej2 | 248430ej2 | \([1, 0, 1, 455282, 49570406]\) | \(53582633/36450\) | \(-7099700143254796350\) | \([2]\) | \(6193152\) | \(2.3059\) |
Rank
sage: E.rank()
The elliptic curves in class 248430.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 248430.ej do not have complex multiplication.Modular form 248430.2.a.ej
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.