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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 364650j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.j1 | 364650j1 | \([1, 1, 0, -7130200, -6291896000]\) | \(20525743802277925973/3130368760037376\) | \(6114001484448000000000\) | \([2]\) | \(27955200\) | \(2.9042\) | \(\Gamma_0(N)\)-optimal |
364650.j2 | 364650j2 | \([1, 1, 0, 12309800, -34577096000]\) | \(105620108359694738347/325643393533670784\) | \(-636022252995450750000000\) | \([2]\) | \(55910400\) | \(3.2507\) |
Rank
sage: E.rank()
The elliptic curves in class 364650j have rank \(1\).
Complex multiplication
The elliptic curves in class 364650j do not have complex multiplication.Modular form 364650.2.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.