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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 440818bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.bb2 | 440818bb1 | \([1, 1, 1, 47202, 18587099]\) | \(4533086375/60669952\) | \(-155662498079162368\) | \([2]\) | \(5806080\) | \(1.9796\) | \(\Gamma_0(N)\)-optimal* |
440818.bb1 | 440818bb2 | \([1, 1, 1, -828958, 271622107]\) | \(24553362849625/1755162752\) | \(4503267424899517568\) | \([2]\) | \(11612160\) | \(2.3262\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 440818bb have rank \(0\).
Complex multiplication
The elliptic curves in class 440818bb do not have complex multiplication.Modular form 440818.2.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 Cremona 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 Cremona labels.