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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 47190b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.f2 | 47190b1 | \([1, 1, 0, -220948, 40423552]\) | \(-673350049820449/10617750000\) | \(-18809991807750000\) | \([2]\) | \(552960\) | \(1.9241\) | \(\Gamma_0(N)\)-optimal |
47190.f1 | 47190b2 | \([1, 1, 0, -3548448, 2571320052]\) | \(2789222297765780449/677605500\) | \(1200419477185500\) | \([2]\) | \(1105920\) | \(2.2707\) |
Rank
sage: E.rank()
The elliptic curves in class 47190b have rank \(0\).
Complex multiplication
The elliptic curves in class 47190b do not have complex multiplication.Modular form 47190.2.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 Cremona 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 Cremona labels.