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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 175450bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
175450.cn2 | 175450bb1 | \([1, 0, 0, 15062, -1180508]\) | \(13651919/29696\) | \(-822004304000000\) | \([]\) | \(756000\) | \(1.5461\) | \(\Gamma_0(N)\)-optimal |
175450.cn1 | 175450bb2 | \([1, 0, 0, -1376438, 625659992]\) | \(-10418796526321/82044596\) | \(-2271046977099312500\) | \([]\) | \(3780000\) | \(2.3508\) |
Rank
sage: E.rank()
The elliptic curves in class 175450bb have rank \(0\).
Complex multiplication
The elliptic curves in class 175450bb do not have complex multiplication.Modular form 175450.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.