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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9464d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9464.c4 | 9464d1 | \([0, 0, 0, 169, 4394]\) | \(432/7\) | \(-8649641728\) | \([2]\) | \(4608\) | \(0.58729\) | \(\Gamma_0(N)\)-optimal |
| 9464.c3 | 9464d2 | \([0, 0, 0, -3211, 65910]\) | \(740772/49\) | \(242189968384\) | \([2, 2]\) | \(9216\) | \(0.93387\) | |
| 9464.c2 | 9464d3 | \([0, 0, 0, -9971, -303186]\) | \(11090466/2401\) | \(23734616901632\) | \([2]\) | \(18432\) | \(1.2804\) | |
| 9464.c1 | 9464d4 | \([0, 0, 0, -50531, 4372030]\) | \(1443468546/7\) | \(69197133824\) | \([2]\) | \(18432\) | \(1.2804\) |
Rank
sage: E.rank()
The elliptic curves in class 9464d have rank \(0\).
Complex multiplication
The elliptic curves in class 9464d do not have complex multiplication.Modular form 9464.2.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 Cremona 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 Cremona labels.
