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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6930.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.n1 | 6930e4 | \([1, -1, 0, -40839, -2960515]\) | \(382704614800227/27778076480\) | \(546755879355840\) | \([2]\) | \(41472\) | \(1.5744\) | |
| 6930.n2 | 6930e2 | \([1, -1, 0, -7764, 264420]\) | \(1917114236485083/7117764500\) | \(192179641500\) | \([6]\) | \(13824\) | \(1.0251\) | |
| 6930.n3 | 6930e1 | \([1, -1, 0, -264, 7920]\) | \(-75526045083/943250000\) | \(-25467750000\) | \([6]\) | \(6912\) | \(0.67848\) | \(\Gamma_0(N)\)-optimal |
| 6930.n4 | 6930e3 | \([1, -1, 0, 2361, -204355]\) | \(73929353373/954060800\) | \(-18778778726400\) | \([2]\) | \(20736\) | \(1.2278\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.n have rank \(1\).
Complex multiplication
The elliptic curves in class 6930.n do not have complex multiplication.Modular form 6930.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
