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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 82800.fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82800.fm1 | 82800bb2 | \([0, 0, 0, -192675, 29749250]\) | \(33909572018/3234375\) | \(75451500000000000\) | \([2]\) | \(1032192\) | \(1.9763\) | |
82800.fm2 | 82800bb1 | \([0, 0, 0, 14325, 2218250]\) | \(27871484/198375\) | \(-2313846000000000\) | \([2]\) | \(516096\) | \(1.6298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 82800.fm have rank \(0\).
Complex multiplication
The elliptic curves in class 82800.fm do not have complex multiplication.Modular form 82800.2.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.