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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2856.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2856.d1 | 2856c3 | \([0, 1, 0, -544, -4624]\) | \(17418812548/1753941\) | \(1796035584\) | \([2]\) | \(1280\) | \(0.51187\) | |
| 2856.d2 | 2856c2 | \([0, 1, 0, -124, 416]\) | \(830321872/127449\) | \(32626944\) | \([2, 2]\) | \(640\) | \(0.16530\) | |
| 2856.d3 | 2856c1 | \([0, 1, 0, -119, 462]\) | \(11745974272/357\) | \(5712\) | \([2]\) | \(320\) | \(-0.18127\) | \(\Gamma_0(N)\)-optimal |
| 2856.d4 | 2856c4 | \([0, 1, 0, 216, 2592]\) | \(1083360092/3306177\) | \(-3385525248\) | \([4]\) | \(1280\) | \(0.51187\) |
Rank
sage: E.rank()
The elliptic curves in class 2856.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2856.d do not have complex multiplication.Modular form 2856.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
