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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 24150bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.bk1 | 24150bf1 | \([1, 0, 1, -129126, -17857352]\) | \(15238420194810961/12619514880\) | \(197179920000000\) | \([2]\) | \(161280\) | \(1.6713\) | \(\Gamma_0(N)\)-optimal |
24150.bk2 | 24150bf2 | \([1, 0, 1, -101126, -25809352]\) | \(-7319577278195281/14169067365600\) | \(-221391677587500000\) | \([2]\) | \(322560\) | \(2.0179\) |
Rank
sage: E.rank()
The elliptic curves in class 24150bf have rank \(1\).
Complex multiplication
The elliptic curves in class 24150bf do not have complex multiplication.Modular form 24150.2.a.bf
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.