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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 39600m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.bb1 | 39600m1 | \([0, 0, 0, -1803675, -932363750]\) | \(55635379958596/24057\) | \(280600848000000\) | \([2]\) | \(430080\) | \(2.1147\) | \(\Gamma_0(N)\)-optimal |
| 39600.bb2 | 39600m2 | \([0, 0, 0, -1794675, -942128750]\) | \(-27403349188178/578739249\) | \(-13500829200672000000\) | \([2]\) | \(860160\) | \(2.4613\) |
Rank
sage: E.rank()
The elliptic curves in class 39600m have rank \(0\).
Complex multiplication
The elliptic curves in class 39600m do not have complex multiplication.Modular form 39600.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
