Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3264.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3264.d1 | 3264v4 | \([0, -1, 0, -6529, 205249]\) | \(939464338184/153\) | \(5013504\) | \([4]\) | \(2048\) | \(0.68727\) | |
| 3264.d2 | 3264v3 | \([0, -1, 0, -769, -2975]\) | \(1536800264/751689\) | \(24631345152\) | \([2]\) | \(2048\) | \(0.68727\) | |
| 3264.d3 | 3264v2 | \([0, -1, 0, -409, 3289]\) | \(1851804352/23409\) | \(95883264\) | \([2, 2]\) | \(1024\) | \(0.34070\) | |
| 3264.d4 | 3264v1 | \([0, -1, 0, -4, 130]\) | \(-140608/111537\) | \(-7138368\) | \([2]\) | \(512\) | \(-0.0058749\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3264.d have rank \(1\).
Complex multiplication
The elliptic curves in class 3264.d do not have complex multiplication.Modular form 3264.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
