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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3920.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3920.h1 | 3920bf3 | \([0, 1, 0, -2025, -35750]\) | \(488095744/125\) | \(235298000\) | \([2]\) | \(2160\) | \(0.59231\) | |
| 3920.h2 | 3920bf4 | \([0, 1, 0, -1780, -44472]\) | \(-20720464/15625\) | \(-470596000000\) | \([2]\) | \(4320\) | \(0.93888\) | |
| 3920.h3 | 3920bf1 | \([0, 1, 0, -65, 118]\) | \(16384/5\) | \(9411920\) | \([2]\) | \(720\) | \(0.043005\) | \(\Gamma_0(N)\)-optimal |
| 3920.h4 | 3920bf2 | \([0, 1, 0, 180, 1000]\) | \(21296/25\) | \(-752953600\) | \([2]\) | \(1440\) | \(0.38958\) |
Rank
sage: E.rank()
The elliptic curves in class 3920.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.h do not have complex multiplication.Modular form 3920.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
