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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 41382bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41382.bn1 | 41382bl1 | \([1, -1, 1, -22529, -1298041]\) | \(-26436959739/50578\) | \(-2419254330966\) | \([]\) | \(172800\) | \(1.2657\) | \(\Gamma_0(N)\)-optimal |
41382.bn2 | 41382bl2 | \([1, -1, 1, 37366, -6411743]\) | \(165469149/603592\) | \(-21047032827305496\) | \([]\) | \(518400\) | \(1.8150\) |
Rank
sage: E.rank()
The elliptic curves in class 41382bl have rank \(1\).
Complex multiplication
The elliptic curves in class 41382bl do not have complex multiplication.Modular form 41382.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.