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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 366300.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366300.h1 | 366300h4 | \([0, 0, 0, -67330575, -195739490250]\) | \(428755198098275568/37894797015625\) | \(2983533158634187500000000\) | \([2]\) | \(39813120\) | \(3.4364\) | |
| 366300.h2 | 366300h3 | \([0, 0, 0, -14596200, 17992931625]\) | \(69889482952409088/12023193359375\) | \(59163128723144531250000\) | \([2]\) | \(19906560\) | \(3.0899\) | |
| 366300.h3 | 366300h2 | \([0, 0, 0, -13939575, 19983422750]\) | \(2773630186458788592/7761322387225\) | \(838222817820300000000\) | \([2]\) | \(13271040\) | \(2.8871\) | |
| 366300.h4 | 366300h1 | \([0, 0, 0, -13930200, 20011707125]\) | \(44288604333860585472/348239375\) | \(2350615781250000\) | \([2]\) | \(6635520\) | \(2.5406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 366300.h have rank \(0\).
Complex multiplication
The elliptic curves in class 366300.h do not have complex multiplication.Modular form 366300.2.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.
