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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 64400.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64400.j1 | 64400v2 | \([0, 1, 0, -424208, -15646412]\) | \(263822189935250/149429406721\) | \(4781741015072000000\) | \([2]\) | \(1105920\) | \(2.2742\) | |
64400.j2 | 64400v1 | \([0, 1, 0, 104792, -1892412]\) | \(7953970437500/4703287687\) | \(-75252602992000000\) | \([2]\) | \(552960\) | \(1.9277\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.j have rank \(1\).
Complex multiplication
The elliptic curves in class 64400.j do not have complex multiplication.Modular form 64400.2.a.j
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.