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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 374850ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.ca1 | 374850ca1 | \([1, -1, 0, -605502, 181512036]\) | \(-4768951705/272\) | \(-1400286304342800\) | \([]\) | \(2903040\) | \(1.9702\) | \(\Gamma_0(N)\)-optimal |
374850.ca2 | 374850ca2 | \([1, -1, 0, -65277, 489764421]\) | \(-5975305/20123648\) | \(-103598781940497715200\) | \([]\) | \(8709120\) | \(2.5195\) |
Rank
sage: E.rank()
The elliptic curves in class 374850ca have rank \(0\).
Complex multiplication
The elliptic curves in class 374850ca do not have complex multiplication.Modular form 374850.2.a.ca
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.