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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 15600.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.q1 | 15600h1 | \([0, -1, 0, -16283, -745938]\) | \(1909913257984/129730653\) | \(32432663250000\) | \([2]\) | \(38400\) | \(1.3411\) | \(\Gamma_0(N)\)-optimal |
| 15600.q2 | 15600h2 | \([0, -1, 0, 14092, -3236688]\) | \(77366117936/1172914587\) | \(-4691658348000000\) | \([2]\) | \(76800\) | \(1.6877\) |
Rank
sage: E.rank()
The elliptic curves in class 15600.q have rank \(0\).
Complex multiplication
The elliptic curves in class 15600.q do not have complex multiplication.Modular form 15600.2.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 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.
