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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2601.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2601.j1 | 2601h1 | \([1, -1, 0, -59877, -3934008]\) | \(274625/81\) | \(7002495519271353\) | \([2]\) | \(13056\) | \(1.7462\) | \(\Gamma_0(N)\)-optimal |
2601.j2 | 2601h2 | \([1, -1, 0, 161208, -26352027]\) | \(5359375/6561\) | \(-567202137060979593\) | \([2]\) | \(26112\) | \(2.0928\) |
Rank
sage: E.rank()
The elliptic curves in class 2601.j have rank \(0\).
Complex multiplication
The elliptic curves in class 2601.j do not have complex multiplication.Modular form 2601.2.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.