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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 363090.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363090.p1 | 363090p4 | \([1, 1, 0, -354414183, -2568262435227]\) | \(41847426343740843075980521/36469612498410000\) | \(4290613440825438090000\) | \([2]\) | \(75497472\) | \(3.4514\) | |
| 363090.p2 | 363090p3 | \([1, 1, 0, -52472263, 90246853957]\) | \(135807848460546664084201/48671921981424334320\) | \(5726202949192591508413680\) | \([2]\) | \(75497472\) | \(3.4514\) | |
| 363090.p3 | 363090p2 | \([1, 1, 0, -22307863, -39538493483]\) | \(10435407396244021837801/301392303902726400\) | \(35458503161851858233600\) | \([2, 2]\) | \(37748736\) | \(3.1048\) | |
| 363090.p4 | 363090p1 | \([1, 1, 0, 334057, -2048002347]\) | \(35042507142352919/15423638227845120\) | \(-1814575613867750522880\) | \([2]\) | \(18874368\) | \(2.7583\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363090.p have rank \(1\).
Complex multiplication
The elliptic curves in class 363090.p do not have complex multiplication.Modular form 363090.2.a.p
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.
