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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 181944.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
181944.bu1 | 181944cr2 | \([0, 0, 0, -360639, 83336850]\) | \(21882096/7\) | \(1659399303695616\) | \([2]\) | \(1327104\) | \(1.8952\) | |
181944.bu2 | 181944cr1 | \([0, 0, 0, -19494, 1666737]\) | \(-55296/49\) | \(-725987195366832\) | \([2]\) | \(663552\) | \(1.5487\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 181944.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 181944.bu do not have complex multiplication.Modular form 181944.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.