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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 485520.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.f1 | 485520f2 | \([0, -1, 0, -189387576, 1003234980720]\) | \(7598444481718798681/108756480\) | \(10752479396647403520\) | \([2]\) | \(63700992\) | \(3.2049\) | \(\Gamma_0(N)\)-optimal* |
485520.f2 | 485520f1 | \([0, -1, 0, -11825976, 15708386160]\) | \(-1850040570997081/7018905600\) | \(-693941527447496294400\) | \([2]\) | \(31850496\) | \(2.8583\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.f have rank \(0\).
Complex multiplication
The elliptic curves in class 485520.f do not have complex multiplication.Modular form 485520.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.