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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 77616fh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.fi4 | 77616fh1 | \([0, 0, 0, -14259, -11662]\) | \(912673/528\) | \(185485360693248\) | \([2]\) | \(221184\) | \(1.4273\) | \(\Gamma_0(N)\)-optimal |
77616.fi2 | 77616fh2 | \([0, 0, 0, -155379, 23498930]\) | \(1180932193/4356\) | \(1530254225719296\) | \([2, 2]\) | \(442368\) | \(1.7739\) | |
77616.fi3 | 77616fh3 | \([0, 0, 0, -84819, 44935058]\) | \(-192100033/2371842\) | \(-833223425904156672\) | \([2]\) | \(884736\) | \(2.1205\) | |
77616.fi1 | 77616fh4 | \([0, 0, 0, -2483859, 1506740690]\) | \(4824238966273/66\) | \(23185670086656\) | \([2]\) | \(884736\) | \(2.1205\) |
Rank
sage: E.rank()
The elliptic curves in class 77616fh have rank \(0\).
Complex multiplication
The elliptic curves in class 77616fh do not have complex multiplication.Modular form 77616.2.a.fh
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.