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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 15979.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15979.e1 | 15979a3 | \([0, -1, 1, -647009, -200099543]\) | \(-50357871050752/19\) | \(-11301643099\) | \([]\) | \(72576\) | \(1.7171\) | |
15979.e2 | 15979a2 | \([0, -1, 1, -7849, -282148]\) | \(-89915392/6859\) | \(-4079893158739\) | \([]\) | \(24192\) | \(1.1678\) | |
15979.e3 | 15979a1 | \([0, -1, 1, 561, -413]\) | \(32768/19\) | \(-11301643099\) | \([]\) | \(8064\) | \(0.61847\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15979.e have rank \(1\).
Complex multiplication
The elliptic curves in class 15979.e do not have complex multiplication.Modular form 15979.2.a.e
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.