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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 320.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 320.d1 | 320a3 | \([0, 0, 0, -428, 3408]\) | \(132304644/5\) | \(327680\) | \([2]\) | \(64\) | \(0.14436\) | |
| 320.d2 | 320a2 | \([0, 0, 0, -28, 48]\) | \(148176/25\) | \(409600\) | \([2, 2]\) | \(32\) | \(-0.20221\) | |
| 320.d3 | 320a1 | \([0, 0, 0, -8, -8]\) | \(55296/5\) | \(5120\) | \([2]\) | \(16\) | \(-0.54879\) | \(\Gamma_0(N)\)-optimal |
| 320.d4 | 320a4 | \([0, 0, 0, 52, 272]\) | \(237276/625\) | \(-40960000\) | \([2]\) | \(64\) | \(0.14436\) |
Rank
sage: E.rank()
The elliptic curves in class 320.d have rank \(0\).
Complex multiplication
The elliptic curves in class 320.d do not have complex multiplication.Modular form 320.2.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.
