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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1014.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1014.g1 | 1014g4 | \([1, 0, 0, -11998412, 15995824272]\) | \(18013780041269221/9216\) | \(97731066221568\) | \([2]\) | \(31200\) | \(2.4525\) | |
| 1014.g2 | 1014g3 | \([1, 0, 0, -749772, 249978000]\) | \(-4395631034341/3145728\) | \(-33358870603628544\) | \([2]\) | \(15600\) | \(2.1059\) | |
| 1014.g3 | 1014g2 | \([1, 0, 0, -35747, -987507]\) | \(476379541/236196\) | \(2504740333905108\) | \([2]\) | \(6240\) | \(1.6478\) | |
| 1014.g4 | 1014g1 | \([1, 0, 0, 8193, -117495]\) | \(5735339/3888\) | \(-41230293562224\) | \([2]\) | \(3120\) | \(1.3012\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1014.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1014.g do not have complex multiplication.Modular form 1014.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
