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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 6930.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.j1 | 6930l1 | \([1, -1, 0, -54, 0]\) | \(24137569/13860\) | \(10103940\) | \([2]\) | \(1536\) | \(0.033680\) | \(\Gamma_0(N)\)-optimal |
6930.j2 | 6930l2 | \([1, -1, 0, 216, -162]\) | \(1524845951/889350\) | \(-648336150\) | \([2]\) | \(3072\) | \(0.38025\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.j have rank \(1\).
Complex multiplication
The elliptic curves in class 6930.j do not have complex multiplication.Modular form 6930.2.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.