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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3786.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3786.f1 | 3786g2 | \([1, 0, 0, -25216170, -48740001444]\) | \(-1773213725647991143081061281/64821906801313848\) | \(-64821906801313848\) | \([]\) | \(304800\) | \(2.7199\) | |
3786.f2 | 3786g1 | \([1, 0, 0, 33150, -12705084]\) | \(4028779434780453599/72094874239991808\) | \(-72094874239991808\) | \([5]\) | \(60960\) | \(1.9152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3786.f have rank \(0\).
Complex multiplication
The elliptic curves in class 3786.f do not have complex multiplication.Modular form 3786.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.