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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 146523.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 146523.p1 | 146523n4 | \([1, 0, 0, -3395467, -2408450812]\) | \(37159393753/1053\) | \(122682329357549013\) | \([2]\) | \(3440640\) | \(2.3807\) | |
| 146523.p2 | 146523n3 | \([1, 0, 0, -953417, 324398502]\) | \(822656953/85683\) | \(9982706577723525243\) | \([2]\) | \(3440640\) | \(2.3807\) | |
| 146523.p3 | 146523n2 | \([1, 0, 0, -220802, -34436325]\) | \(10218313/1521\) | \(177207809072015241\) | \([2, 2]\) | \(1720320\) | \(2.0341\) | |
| 146523.p4 | 146523n1 | \([1, 0, 0, 23403, -2933880]\) | \(12167/39\) | \(-4543789976205519\) | \([2]\) | \(860160\) | \(1.6876\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 146523.p have rank \(0\).
Complex multiplication
The elliptic curves in class 146523.p do not have complex multiplication.Modular form 146523.2.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.
