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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1254.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1254.j1 | 1254k2 | \([1, 0, 0, -12285, -545847]\) | \(-205046048384508241/9570677281176\) | \(-9570677281176\) | \([]\) | \(3000\) | \(1.2540\) | |
1254.j2 | 1254k1 | \([1, 0, 0, 75, 1953]\) | \(46617130799/1664188416\) | \(-1664188416\) | \([5]\) | \(600\) | \(0.44930\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1254.j have rank \(0\).
Complex multiplication
The elliptic curves in class 1254.j do not have complex multiplication.Modular form 1254.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.