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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 463704b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463704.b1 | 463704b1 | \([0, -1, 0, -24119048, -45583227396]\) | \(210094874500/3753\) | \(27718346698335470592\) | \([2]\) | \(25966080\) | \(2.8578\) | \(\Gamma_0(N)\)-optimal |
463704.b2 | 463704b2 | \([0, -1, 0, -23346208, -48641509844]\) | \(-95269531250/14085009\) | \(-208053910317706042263552\) | \([2]\) | \(51932160\) | \(3.2043\) |
Rank
sage: E.rank()
The elliptic curves in class 463704b have rank \(1\).
Complex multiplication
The elliptic curves in class 463704b do not have complex multiplication.Modular form 463704.2.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.