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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 397800.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.cf1 | 397800cf3 | \([0, 0, 0, -7356675, 7680086750]\) | \(1887517194957938/21849165\) | \(509697321120000000\) | \([2]\) | \(9437184\) | \(2.5489\) | |
| 397800.cf2 | 397800cf2 | \([0, 0, 0, -471675, 113471750]\) | \(994958062276/98903025\) | \(1153604883600000000\) | \([2, 2]\) | \(4718592\) | \(2.2023\) | |
| 397800.cf3 | 397800cf1 | \([0, 0, 0, -107175, -11551750]\) | \(46689225424/7249905\) | \(21140722980000000\) | \([2]\) | \(2359296\) | \(1.8557\) | \(\Gamma_0(N)\)-optimal |
| 397800.cf4 | 397800cf4 | \([0, 0, 0, 581325, 548360750]\) | \(931329171502/6107473125\) | \(-142475133060000000000\) | \([2]\) | \(9437184\) | \(2.5489\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.cf do not have complex multiplication.Modular form 397800.2.a.cf
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
