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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 10080.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10080.p1 | 10080v1 | \([0, 0, 0, -12333, 527168]\) | \(4446542056384/25725\) | \(1200225600\) | \([2]\) | \(15360\) | \(0.93250\) | \(\Gamma_0(N)\)-optimal |
10080.p2 | 10080v2 | \([0, 0, 0, -12108, 547328]\) | \(-65743598656/5294205\) | \(-15808411422720\) | \([2]\) | \(30720\) | \(1.2791\) |
Rank
sage: E.rank()
The elliptic curves in class 10080.p have rank \(1\).
Complex multiplication
The elliptic curves in class 10080.p do not have complex multiplication.Modular form 10080.2.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 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.