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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 348174bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348174.bu1 | 348174bu1 | \([1, -1, 1, -696506, -226132167]\) | \(-86175179713/1152576\) | \(-499787152254149184\) | \([]\) | \(9676800\) | \(2.2037\) | \(\Gamma_0(N)\)-optimal |
348174.bu2 | 348174bu2 | \([1, -1, 1, 2482474, -1144221591]\) | \(3901777377407/3560891556\) | \(-1544095877633306780004\) | \([]\) | \(29030400\) | \(2.7530\) |
Rank
sage: E.rank()
The elliptic curves in class 348174bu have rank \(0\).
Complex multiplication
The elliptic curves in class 348174bu do not have complex multiplication.Modular form 348174.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.