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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 71148.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71148.bj1 | 71148cv2 | \([0, 1, 0, -215420, -38454396]\) | \(20720464/63\) | \(3361436146075392\) | \([2]\) | \(806400\) | \(1.8479\) | |
| 71148.bj2 | 71148cv1 | \([0, 1, 0, -7905, -1101696]\) | \(-16384/147\) | \(-490209437969328\) | \([2]\) | \(403200\) | \(1.5013\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 71148.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 71148.bj do not have complex multiplication.Modular form 71148.2.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.
