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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 28899.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28899.m1 | 28899k4 | \([1, -1, 0, -154413, -23315850]\) | \(115714886617/1539\) | \(5415346648179\) | \([2]\) | \(92160\) | \(1.5868\) | |
| 28899.m2 | 28899k2 | \([1, -1, 0, -9918, -341145]\) | \(30664297/3249\) | \(11432398479489\) | \([2, 2]\) | \(46080\) | \(1.2402\) | |
| 28899.m3 | 28899k1 | \([1, -1, 0, -2313, 37584]\) | \(389017/57\) | \(200568394377\) | \([2]\) | \(23040\) | \(0.89363\) | \(\Gamma_0(N)\)-optimal |
| 28899.m4 | 28899k3 | \([1, -1, 0, 12897, -1696356]\) | \(67419143/390963\) | \(-1375698617031843\) | \([2]\) | \(92160\) | \(1.5868\) |
Rank
sage: E.rank()
The elliptic curves in class 28899.m have rank \(1\).
Complex multiplication
The elliptic curves in class 28899.m do not have complex multiplication.Modular form 28899.2.a.m
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.
