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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 65520.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.d1 | 65520t4 | \([0, 0, 0, -11163, 323962]\) | \(206081497444/58524375\) | \(43688211840000\) | \([2]\) | \(163840\) | \(1.3241\) | |
| 65520.d2 | 65520t2 | \([0, 0, 0, -4143, -98642]\) | \(42140629456/1863225\) | \(347722502400\) | \([2, 2]\) | \(81920\) | \(0.97750\) | |
| 65520.d3 | 65520t1 | \([0, 0, 0, -4098, -100973]\) | \(652517349376/1365\) | \(15921360\) | \([2]\) | \(40960\) | \(0.63093\) | \(\Gamma_0(N)\)-optimal |
| 65520.d4 | 65520t3 | \([0, 0, 0, 2157, -372062]\) | \(1486779836/80970435\) | \(-60444105845760\) | \([2]\) | \(163840\) | \(1.3241\) |
Rank
sage: E.rank()
The elliptic curves in class 65520.d have rank \(1\).
Complex multiplication
The elliptic curves in class 65520.d do not have complex multiplication.Modular form 65520.2.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.
