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SageMath
E = EllipticCurve("hf1")
E.isogeny_class()
Elliptic curves in class 179520hf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.de3 | 179520hf1 | \([0, -1, 0, -8865, -266463]\) | \(293946977449/50490000\) | \(13235650560000\) | \([2]\) | \(442368\) | \(1.2382\) | \(\Gamma_0(N)\)-optimal |
| 179520.de2 | 179520hf2 | \([0, -1, 0, -40865, 2939937]\) | \(28790481449449/2549240100\) | \(668267996774400\) | \([2, 2]\) | \(884736\) | \(1.5848\) | |
| 179520.de1 | 179520hf3 | \([0, -1, 0, -639265, 196941217]\) | \(110211585818155849/993794670\) | \(260517309972480\) | \([2]\) | \(1769472\) | \(1.9313\) | |
| 179520.de4 | 179520hf4 | \([0, -1, 0, 45535, 13636257]\) | \(39829997144951/330164359470\) | \(-86550605848903680\) | \([2]\) | \(1769472\) | \(1.9313\) |
Rank
sage: E.rank()
The elliptic curves in class 179520hf have rank \(0\).
Complex multiplication
The elliptic curves in class 179520hf do not have complex multiplication.Modular form 179520.2.a.hf
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.
