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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 284592fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 284592.fh2 | 284592fh1 | \([0, -1, 0, 45456, -4590144]\) | \(596183/864\) | \(-15052961866973184\) | \([]\) | \(1944000\) | \(1.7897\) | \(\Gamma_0(N)\)-optimal |
| 284592.fh1 | 284592fh2 | \([0, -1, 0, -1377504, -625000704]\) | \(-16591834777/98304\) | \(-1712692550197837824\) | \([]\) | \(5832000\) | \(2.3390\) |
Rank
sage: E.rank()
The elliptic curves in class 284592fh have rank \(1\).
Complex multiplication
The elliptic curves in class 284592fh do not have complex multiplication.Modular form 284592.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
