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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 93654.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93654.bl1 | 93654bh2 | \([1, -1, 1, -65232212, -202795274437]\) | \(-23769846831649063249/3261823333284\) | \(-4212540355473097580196\) | \([]\) | \(11195520\) | \(3.1672\) | |
93654.bl2 | 93654bh1 | \([1, -1, 1, 173128, 61903163]\) | \(444369620591/1540767744\) | \(-1989852189044391936\) | \([]\) | \(1599360\) | \(2.1942\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93654.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 93654.bl do not have complex multiplication.Modular form 93654.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.