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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 8379.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8379.j1 | 8379f3 | \([0, 0, 1, -339276, -76063766]\) | \(-50357871050752/19\) | \(-1629556299\) | \([]\) | \(27216\) | \(1.5557\) | |
8379.j2 | 8379f2 | \([0, 0, 1, -4116, -108131]\) | \(-89915392/6859\) | \(-588269823939\) | \([]\) | \(9072\) | \(1.0064\) | |
8379.j3 | 8379f1 | \([0, 0, 1, 294, -86]\) | \(32768/19\) | \(-1629556299\) | \([]\) | \(3024\) | \(0.45709\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8379.j have rank \(1\).
Complex multiplication
The elliptic curves in class 8379.j do not have complex multiplication.Modular form 8379.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.