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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 229320.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.cs1 | 229320f2 | \([0, 0, 0, -964028667, 4982359629926]\) | \(386965237776463086681532/182055746334444328125\) | \(46615033040577332136624000000\) | \([2]\) | \(167608320\) | \(4.1952\) | |
| 229320.cs2 | 229320f1 | \([0, 0, 0, -496199487, -4200846475966]\) | \(211072197308055014773168/3052652281946850375\) | \(195406475556854808503712000\) | \([2]\) | \(83804160\) | \(3.8486\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229320.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 229320.cs do not have complex multiplication.Modular form 229320.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
