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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 6930.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.h1 | 6930k4 | \([1, -1, 0, -95040009, 356645502765]\) | \(130231365028993807856757649/4753980000\) | \(3465651420000\) | \([2]\) | \(491520\) | \(2.8245\) | |
| 6930.h2 | 6930k3 | \([1, -1, 0, -6050889, 5354872173]\) | \(33608860073906150870929/2466782226562500000\) | \(1798284243164062500000\) | \([2]\) | \(491520\) | \(2.8245\) | |
| 6930.h3 | 6930k2 | \([1, -1, 0, -5940009, 5573682765]\) | \(31794905164720991157649/192099600000000\) | \(140040608400000000\) | \([2, 2]\) | \(245760\) | \(2.4779\) | |
| 6930.h4 | 6930k1 | \([1, -1, 0, -364329, 90559053]\) | \(-7336316844655213969/604492922880000\) | \(-440675340779520000\) | \([2]\) | \(122880\) | \(2.1314\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6930.h have rank \(1\).
Complex multiplication
The elliptic curves in class 6930.h do not have complex multiplication.Modular form 6930.2.a.h
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.
