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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4200.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4200.x1 | 4200bb1 | \([0, 1, 0, -15428, -742752]\) | \(12692020761488/9261\) | \(296352000\) | \([2]\) | \(4608\) | \(0.93668\) | \(\Gamma_0(N)\)-optimal |
4200.x2 | 4200bb2 | \([0, 1, 0, -15328, -752752]\) | \(-3111705953492/85766121\) | \(-10978063488000\) | \([2]\) | \(9216\) | \(1.2833\) |
Rank
sage: E.rank()
The elliptic curves in class 4200.x have rank \(0\).
Complex multiplication
The elliptic curves in class 4200.x do not have complex multiplication.Modular form 4200.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.