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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 14450.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.b1 | 14450p2 | \([1, 0, 1, -190891, -36002922]\) | \(-882216989/131072\) | \(-114290809913344000\) | \([]\) | \(208080\) | \(2.0030\) | |
14450.b2 | 14450p1 | \([1, 0, 1, -3041, 64278]\) | \(-297756989/2\) | \(-20880250\) | \([]\) | \(12240\) | \(0.58638\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14450.b have rank \(1\).
Complex multiplication
The elliptic curves in class 14450.b do not have complex multiplication.Modular form 14450.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 17 \\ 17 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.