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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 290145.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290145.x1 | 290145x2 | \([1, 0, 1, -1160598, 481029631]\) | \(290656902035521/86293125\) | \(51329163191968125\) | \([2]\) | \(4945920\) | \(2.1849\) | |
290145.x2 | 290145x1 | \([1, 0, 1, -63093, 9541483]\) | \(-46694890801/39169575\) | \(-23298976683658575\) | \([2]\) | \(2472960\) | \(1.8384\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 290145.x have rank \(0\).
Complex multiplication
The elliptic curves in class 290145.x do not have complex multiplication.Modular form 290145.2.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.