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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 159936.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159936.bg1 | 159936io2 | \([0, -1, 0, -4094523169, -100843240667231]\) | \(717647917494305598319/844621814448\) | \(8934794661425712709238784\) | \([2]\) | \(86704128\) | \(4.0704\) | |
| 159936.bg2 | 159936io1 | \([0, -1, 0, -253801249, -1602826976351]\) | \(-170915990723796079/6015674034432\) | \(-63636542803299112379744256\) | \([2]\) | \(43352064\) | \(3.7238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159936.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 159936.bg do not have complex multiplication.Modular form 159936.2.a.bg
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.
