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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 147294.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147294.bj1 | 147294d2 | \([1, -1, 1, -887522, 322041255]\) | \(901456690969801/10542042\) | \(904150049759082\) | \([2]\) | \(2949120\) | \(2.0204\) | |
147294.bj2 | 147294d1 | \([1, -1, 1, -54032, 5315055]\) | \(-203401212841/23861628\) | \(-2046519274304988\) | \([2]\) | \(1474560\) | \(1.6739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147294.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 147294.bj do not have complex multiplication.Modular form 147294.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.