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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 156702.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
156702.bu1 | 156702bg1 | \([1, 1, 1, -7634495, -8124541531]\) | \(-418288977642645996769/122877464621184\) | \(-14456410835217676416\) | \([]\) | \(6322176\) | \(2.6555\) | \(\Gamma_0(N)\)-optimal |
156702.bu2 | 156702bg2 | \([1, 1, 1, 42364615, 358508096729]\) | \(71473535169369644529791/513262758348672548034\) | \(-60384850256962976603652066\) | \([]\) | \(44255232\) | \(3.6285\) |
Rank
sage: E.rank()
The elliptic curves in class 156702.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 156702.bu do not have complex multiplication.Modular form 156702.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.