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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 6480p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6480.t2 | 6480p1 | \([0, 0, 0, 33, 26]\) | \(191664/125\) | \(-2592000\) | \([]\) | \(864\) | \(-0.080477\) | \(\Gamma_0(N)\)-optimal |
6480.t1 | 6480p2 | \([0, 0, 0, -567, 5346]\) | \(-148176/5\) | \(-680244480\) | \([]\) | \(2592\) | \(0.46883\) |
Rank
sage: E.rank()
The elliptic curves in class 6480p have rank \(1\).
Complex multiplication
The elliptic curves in class 6480p do not have complex multiplication.Modular form 6480.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.