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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 22848.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22848.bb1 | 22848h4 | \([0, -1, 0, -725469697, 7521266762497]\) | \(322159999717985454060440834/4250799\) | \(557160726528\) | \([4]\) | \(2211840\) | \(3.2376\) | |
22848.bb2 | 22848h3 | \([0, -1, 0, -45458497, 116896156993]\) | \(79260902459030376659234/842751810121431609\) | \(110461165256236283854848\) | \([2]\) | \(2211840\) | \(3.2376\) | |
22848.bb3 | 22848h2 | \([0, -1, 0, -45341857, 117531121825]\) | \(157304700372188331121828/18069292138401\) | \(1184189129582247936\) | \([2, 2]\) | \(1105920\) | \(2.8910\) | |
22848.bb4 | 22848h1 | \([0, -1, 0, -2826577, 1847044945]\) | \(-152435594466395827792/1646846627220711\) | \(-26981935140384129024\) | \([2]\) | \(552960\) | \(2.5444\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22848.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 22848.bb do not have complex multiplication.Modular form 22848.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.