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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 17238j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17238.m1 | 17238j1 | \([1, 1, 1, -426, 1971]\) | \(1771561/612\) | \(2954007108\) | \([2]\) | \(15360\) | \(0.51895\) | \(\Gamma_0(N)\)-optimal |
17238.m2 | 17238j2 | \([1, 1, 1, 1264, 15491]\) | \(46268279/46818\) | \(-225981543762\) | \([2]\) | \(30720\) | \(0.86552\) |
Rank
sage: E.rank()
The elliptic curves in class 17238j have rank \(0\).
Complex multiplication
The elliptic curves in class 17238j do not have complex multiplication.Modular form 17238.2.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 Cremona 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 Cremona labels.