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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 296208.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296208.b1 | 296208b1 | \([0, 0, 0, -83127, -4405610]\) | \(192143824/85833\) | \(28377745966893312\) | \([2]\) | \(3686400\) | \(1.8525\) | \(\Gamma_0(N)\)-optimal |
296208.b2 | 296208b2 | \([0, 0, 0, 287133, -32915630]\) | \(1979654684/1499553\) | \(-1983103659333485568\) | \([2]\) | \(7372800\) | \(2.1991\) |
Rank
sage: E.rank()
The elliptic curves in class 296208.b have rank \(1\).
Complex multiplication
The elliptic curves in class 296208.b do not have complex multiplication.Modular form 296208.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.