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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 416955q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 416955.q4 | 416955q1 | \([1, 1, 1, -1139865, -32481618]\) | \(3481467828171481/2005331497785\) | \(94342587010344873585\) | \([2]\) | \(13271040\) | \(2.5224\) | \(\Gamma_0(N)\)-optimal |
| 416955.q2 | 416955q2 | \([1, 1, 1, -12982470, -17966922630]\) | \(5143681768032498601/14238434358225\) | \(669859688443364721225\) | \([2, 2]\) | \(26542080\) | \(2.8689\) | |
| 416955.q3 | 416955q3 | \([1, 1, 1, -7865295, -32268403320]\) | \(-1143792273008057401/8897444448004035\) | \(-418588112704908518129835\) | \([2]\) | \(53084160\) | \(3.2155\) | |
| 416955.q1 | 416955q4 | \([1, 1, 1, -207581325, -1151232814608]\) | \(21026497979043461623321/161783881875\) | \(7611265254409306875\) | \([2]\) | \(53084160\) | \(3.2155\) |
Rank
sage: E.rank()
The elliptic curves in class 416955q have rank \(0\).
Complex multiplication
The elliptic curves in class 416955q do not have complex multiplication.Modular form 416955.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
