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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 224400.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.cs1 | 224400ff4 | \([0, -1, 0, -227179008, -1317878719488]\) | \(20260414982443110947641/720358602480\) | \(46102950558720000000\) | \([2]\) | \(21233664\) | \(3.2689\) | |
| 224400.cs2 | 224400ff2 | \([0, -1, 0, -14219008, -20526399488]\) | \(4967657717692586041/29490113030400\) | \(1887367233945600000000\) | \([2, 2]\) | \(10616832\) | \(2.9223\) | |
| 224400.cs3 | 224400ff3 | \([0, -1, 0, -6059008, -43929279488]\) | \(-384369029857072441/12804787777021680\) | \(-819506417729387520000000\) | \([4]\) | \(21233664\) | \(3.2689\) | |
| 224400.cs4 | 224400ff1 | \([0, -1, 0, -1419008, 107200512]\) | \(4937402992298041/2780405760000\) | \(177945968640000000000\) | \([2]\) | \(5308416\) | \(2.5758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.cs do not have complex multiplication.Modular form 224400.2.a.cs
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
