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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 3822.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3822.x1 | 3822w1 | \([1, 1, 1, -37297, 2756879]\) | \(16728308209329751/16376256\) | \(5617055808\) | \([2]\) | \(8640\) | \(1.1644\) | \(\Gamma_0(N)\)-optimal |
| 3822.x2 | 3822w2 | \([1, 1, 1, -37017, 2800671]\) | \(-16354376146655191/523792501128\) | \(-179660827886904\) | \([2]\) | \(17280\) | \(1.5110\) |
Rank
sage: E.rank()
The elliptic curves in class 3822.x have rank \(0\).
Complex multiplication
The elliptic curves in class 3822.x do not have complex multiplication.Modular form 3822.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
