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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 187200.fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.fl1 | 187200do2 | \([0, 0, 0, -18300, -830000]\) | \(3631696/507\) | \(94618368000000\) | \([2]\) | \(491520\) | \(1.4081\) | |
187200.fl2 | 187200do1 | \([0, 0, 0, -4800, 115000]\) | \(1048576/117\) | \(1364688000000\) | \([2]\) | \(245760\) | \(1.0615\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.fl have rank \(0\).
Complex multiplication
The elliptic curves in class 187200.fl do not have complex multiplication.Modular form 187200.2.a.fl
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.