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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 4800.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4800.p1 | 4800bk2 | \([0, -1, 0, -4853, 131757]\) | \(-30866268160/3\) | \(-1228800\) | \([]\) | \(3456\) | \(0.60179\) | |
4800.p2 | 4800bk1 | \([0, -1, 0, -53, 237]\) | \(-40960/27\) | \(-11059200\) | \([]\) | \(1152\) | \(0.052484\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4800.p have rank \(0\).
Complex multiplication
The elliptic curves in class 4800.p do not have complex multiplication.Modular form 4800.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.