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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 476850n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.n2 | 476850n1 | \([1, 1, 0, 173250, 9976500]\) | \(440680479839/287496000\) | \(-375186772125000000\) | \([]\) | \(6345216\) | \(2.0610\) | \(\Gamma_0(N)\)-optimal |
476850.n1 | 476850n2 | \([1, 1, 0, -1994250, -1266681000]\) | \(-672120501924961/141476861460\) | \(-184629514781260312500\) | \([]\) | \(19035648\) | \(2.6103\) |
Rank
sage: E.rank()
The elliptic curves in class 476850n have rank \(0\).
Complex multiplication
The elliptic curves in class 476850n do not have complex multiplication.Modular form 476850.2.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.