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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 22386x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22386.bc4 | 22386x1 | \([1, 0, 0, -13937, -709527]\) | \(-299387428352690833/43513123110912\) | \(-43513123110912\) | \([2]\) | \(86016\) | \(1.3474\) | \(\Gamma_0(N)\)-optimal |
| 22386.bc3 | 22386x2 | \([1, 0, 0, -230257, -42545815]\) | \(1350088866691276036753/23380861061376\) | \(23380861061376\) | \([2, 2]\) | \(172032\) | \(1.6940\) | |
| 22386.bc2 | 22386x3 | \([1, 0, 0, -237537, -39713895]\) | \(1482236924759943084433/177107469272815536\) | \(177107469272815536\) | \([2]\) | \(344064\) | \(2.0406\) | |
| 22386.bc1 | 22386x4 | \([1, 0, 0, -3684097, -2722034887]\) | \(5529895044677685547285393/1658533968\) | \(1658533968\) | \([2]\) | \(344064\) | \(2.0406\) |
Rank
sage: E.rank()
The elliptic curves in class 22386x have rank \(0\).
Complex multiplication
The elliptic curves in class 22386x do not have complex multiplication.Modular form 22386.2.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 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.
