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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 40656bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40656.x4 | 40656bq1 | \([0, -1, 0, 149032, 13118448]\) | \(50447927375/39517632\) | \(-286752340637908992\) | \([2]\) | \(276480\) | \(2.0378\) | \(\Gamma_0(N)\)-optimal |
40656.x3 | 40656bq2 | \([0, -1, 0, -702808, 113976304]\) | \(5290763640625/2291573592\) | \(16628377207673290752\) | \([2]\) | \(552960\) | \(2.3843\) | |
40656.x2 | 40656bq3 | \([0, -1, 0, -1593368, -982698000]\) | \(-61653281712625/21875235228\) | \(-158733572488195719168\) | \([2]\) | \(829440\) | \(2.5871\) | |
40656.x1 | 40656bq4 | \([0, -1, 0, -27361528, -55075219472]\) | \(312196988566716625/25367712678\) | \(184076085000398266368\) | \([2]\) | \(1658880\) | \(2.9337\) |
Rank
sage: E.rank()
The elliptic curves in class 40656bq have rank \(0\).
Complex multiplication
The elliptic curves in class 40656bq do not have complex multiplication.Modular form 40656.2.a.bq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.