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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 389620n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
389620.n1 | 389620n1 | \([0, 1, 0, -318570050, -2188651436875]\) | \(-126142795384287538429696/9315359375\) | \(-264043637915750000\) | \([]\) | \(38257920\) | \(3.2392\) | \(\Gamma_0(N)\)-optimal |
389620.n2 | 389620n2 | \([0, 1, 0, -315363550, -2234863309175]\) | \(-122372013839654770813696/5297595236711512175\) | \(-150160209842302131524082800\) | \([]\) | \(114773760\) | \(3.7885\) |
Rank
sage: E.rank()
The elliptic curves in class 389620n have rank \(0\).
Complex multiplication
The elliptic curves in class 389620n do not have complex multiplication.Modular form 389620.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.