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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 232562f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
232562.f2 | 232562f1 | \([1, 1, 0, 346421, 29929101]\) | \(24167/16\) | \(-3043908735080655376\) | \([]\) | \(5385600\) | \(2.2354\) | \(\Gamma_0(N)\)-optimal |
232562.f1 | 232562f2 | \([1, 1, 0, -6049034, 5879212244]\) | \(-128667913/4096\) | \(-779240636180647776256\) | \([]\) | \(16156800\) | \(2.7847\) |
Rank
sage: E.rank()
The elliptic curves in class 232562f have rank \(1\).
Complex multiplication
The elliptic curves in class 232562f do not have complex multiplication.Modular form 232562.2.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.