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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 363090.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363090.n1 | 363090n3 | \([1, 1, 0, -22352453, 40666449153]\) | \(10498108899872700356041/5863159165500\) | \(689794812661909500\) | \([2]\) | \(18874368\) | \(2.7500\) | |
| 363090.n2 | 363090n4 | \([1, 1, 0, -3099373, -1181904023]\) | \(27987056667799999561/11078094726562500\) | \(1303326766485351562500\) | \([2]\) | \(18874368\) | \(2.7500\) | |
| 363090.n3 | 363090n2 | \([1, 1, 0, -1404953, 627397653]\) | \(2606881817941196041/60536180250000\) | \(7122021070232250000\) | \([2, 2]\) | \(9437184\) | \(2.4034\) | |
| 363090.n4 | 363090n1 | \([1, 1, 0, 10167, 30500037]\) | \(987750361079/3415452768000\) | \(-401824602702432000\) | \([2]\) | \(4718592\) | \(2.0568\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363090.n have rank \(1\).
Complex multiplication
The elliptic curves in class 363090.n do not have complex multiplication.Modular form 363090.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
