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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 141204q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141204.d4 | 141204q1 | \([0, -1, 0, 11207, -159446]\) | \(2048000/1323\) | \(-100550206573488\) | \([2]\) | \(388800\) | \(1.3757\) | \(\Gamma_0(N)\)-optimal |
| 141204.d3 | 141204q2 | \([0, -1, 0, -47628, -1265544]\) | \(9826000/5103\) | \(6205384177106688\) | \([2]\) | \(777600\) | \(1.7223\) | |
| 141204.d2 | 141204q3 | \([0, -1, 0, -190513, -32898602]\) | \(-10061824000/352947\) | \(-26824560664771632\) | \([2]\) | \(1166400\) | \(1.9250\) | |
| 141204.d1 | 141204q4 | \([0, -1, 0, -3073428, -2072849256]\) | \(2640279346000/3087\) | \(3753874378743552\) | \([2]\) | \(2332800\) | \(2.2716\) |
Rank
sage: E.rank()
The elliptic curves in class 141204q have rank \(0\).
Complex multiplication
The elliptic curves in class 141204q do not have complex multiplication.Modular form 141204.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
