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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 273600q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.q1 | 273600q1 | \([0, 0, 0, -14700, -610000]\) | \(470596/57\) | \(42550272000000\) | \([2]\) | \(819200\) | \(1.3457\) | \(\Gamma_0(N)\)-optimal |
273600.q2 | 273600q2 | \([0, 0, 0, 21300, -3130000]\) | \(715822/3249\) | \(-4850731008000000\) | \([2]\) | \(1638400\) | \(1.6922\) |
Rank
sage: E.rank()
The elliptic curves in class 273600q have rank \(0\).
Complex multiplication
The elliptic curves in class 273600q do not have complex multiplication.Modular form 273600.2.a.q
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.