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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 185130.fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185130.fm1 | 185130t1 | \([1, -1, 1, -1115436587, -14336544541701]\) | \(118843307222596927933249/19794099600000000\) | \(25563445608595712400000000\) | \([2]\) | \(129024000\) | \(3.8831\) | \(\Gamma_0(N)\)-optimal |
185130.fm2 | 185130t2 | \([1, -1, 1, -1006536587, -17247528661701]\) | \(-87323024620536113533249/48975797371840020000\) | \(-63250673561965768422319380000\) | \([2]\) | \(258048000\) | \(4.2297\) |
Rank
sage: E.rank()
The elliptic curves in class 185130.fm have rank \(1\).
Complex multiplication
The elliptic curves in class 185130.fm do not have complex multiplication.Modular form 185130.2.a.fm
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.