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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 102850f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102850.t1 | 102850f1 | \([1, 1, 0, -7625, -1077875]\) | \(-1771561/17000\) | \(-470570890625000\) | \([]\) | \(414720\) | \(1.4978\) | \(\Gamma_0(N)\)-optimal |
102850.t2 | 102850f2 | \([1, 1, 0, 68000, 27584000]\) | \(1256216039/12577280\) | \(-348147167720000000\) | \([]\) | \(1244160\) | \(2.0471\) |
Rank
sage: E.rank()
The elliptic curves in class 102850f have rank \(0\).
Complex multiplication
The elliptic curves in class 102850f do not have complex multiplication.Modular form 102850.2.a.f
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.