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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 87360.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.d1 | 87360eb4 | \([0, -1, 0, -4961, -94335]\) | \(206081497444/58524375\) | \(3835453440000\) | \([2]\) | \(163840\) | \(1.1213\) | |
| 87360.d2 | 87360eb2 | \([0, -1, 0, -1841, 29841]\) | \(42140629456/1863225\) | \(30527078400\) | \([2, 2]\) | \(81920\) | \(0.77477\) | |
| 87360.d3 | 87360eb1 | \([0, -1, 0, -1821, 30525]\) | \(652517349376/1365\) | \(1397760\) | \([2]\) | \(40960\) | \(0.42820\) | \(\Gamma_0(N)\)-optimal |
| 87360.d4 | 87360eb3 | \([0, -1, 0, 959, 109921]\) | \(1486779836/80970435\) | \(-5306478428160\) | \([2]\) | \(163840\) | \(1.1213\) |
Rank
sage: E.rank()
The elliptic curves in class 87360.d have rank \(2\).
Complex multiplication
The elliptic curves in class 87360.d do not have complex multiplication.Modular form 87360.2.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.
