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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 88752.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88752.bj1 | 88752bf2 | \([0, 1, 0, -1772111800, -28717406000044]\) | \(-23769846831649063249/3261823333284\) | \(-84456118236723156676263936\) | \([]\) | \(52157952\) | \(3.9927\) | |
| 88752.bj2 | 88752bf1 | \([0, 1, 0, 4703240, 8772785876]\) | \(444369620591/1540767744\) | \(-39894025355315984203776\) | \([]\) | \(7451136\) | \(3.0197\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88752.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 88752.bj do not have complex multiplication.Modular form 88752.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
