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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 4830.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4830.p1 | 4830o3 | \([1, 0, 1, -2888, -19882]\) | \(2662558086295801/1374177967680\) | \(1374177967680\) | \([2]\) | \(8640\) | \(1.0212\) | |
| 4830.p2 | 4830o1 | \([1, 0, 1, -1613, 24788]\) | \(463702796512201/15214500\) | \(15214500\) | \([6]\) | \(2880\) | \(0.47185\) | \(\Gamma_0(N)\)-optimal |
| 4830.p3 | 4830o2 | \([1, 0, 1, -1543, 27056]\) | \(-405897921250921/84358968750\) | \(-84358968750\) | \([6]\) | \(5760\) | \(0.81842\) | |
| 4830.p4 | 4830o4 | \([1, 0, 1, 10832, -151594]\) | \(140574743422291079/91397357868600\) | \(-91397357868600\) | \([2]\) | \(17280\) | \(1.3677\) |
Rank
sage: E.rank()
The elliptic curves in class 4830.p have rank \(0\).
Complex multiplication
The elliptic curves in class 4830.p do not have complex multiplication.Modular form 4830.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
