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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 436800.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.b1 | 436800b1 | \([0, -1, 0, -7086633, 7263556137]\) | \(614983729942899136/35933625\) | \(2299752000000000\) | \([2]\) | \(12533760\) | \(2.4124\) | \(\Gamma_0(N)\)-optimal |
436800.b2 | 436800b2 | \([0, -1, 0, -7073633, 7291519137]\) | \(-76450685425962632/587722078125\) | \(-300913704000000000000\) | \([2]\) | \(25067520\) | \(2.7590\) |
Rank
sage: E.rank()
The elliptic curves in class 436800.b have rank \(1\).
Complex multiplication
The elliptic curves in class 436800.b do not have complex multiplication.Modular form 436800.2.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.