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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 14490.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.k1 | 14490c1 | \([1, -1, 0, -44339415, 47524672925]\) | \(489781415227546051766883/233890092903563264000\) | \(4603658698620835725312000\) | \([2]\) | \(3096576\) | \(3.4263\) | \(\Gamma_0(N)\)-optimal |
| 14490.k2 | 14490c2 | \([1, -1, 0, 159149865, 361345840541]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-314406593624471491584000000\) | \([2]\) | \(6193152\) | \(3.7729\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.k have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.k do not have complex multiplication.Modular form 14490.2.a.k
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.
