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SageMath
E = EllipticCurve("qa1")
E.isogeny_class()
Elliptic curves in class 273600.qa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.qa1 | 273600qa2 | \([0, 0, 0, -866700, 307574000]\) | \(651038076963/7220000\) | \(798474240000000000\) | \([2]\) | \(5898240\) | \(2.2494\) | |
| 273600.qa2 | 273600qa1 | \([0, 0, 0, -98700, -4234000]\) | \(961504803/486400\) | \(53791948800000000\) | \([2]\) | \(2949120\) | \(1.9029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.qa have rank \(0\).
Complex multiplication
The elliptic curves in class 273600.qa do not have complex multiplication.Modular form 273600.2.a.qa
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.
