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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 389844.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 389844.bt1 | 389844bt3 | \([0, 0, 0, -2184420, -167743807]\) | \(840033089536000/477272151837\) | \(654940497990120228432\) | \([2]\) | \(9953280\) | \(2.6841\) | |
| 389844.bt2 | 389844bt1 | \([0, 0, 0, -1390620, 631184141]\) | \(216727177216000/2738853\) | \(3758412764787408\) | \([2]\) | \(3317760\) | \(2.1348\) | \(\Gamma_0(N)\)-optimal |
| 389844.bt3 | 389844bt2 | \([0, 0, 0, -1353135, 666817382]\) | \(-12479332642000/1526829993\) | \(-33523273197073191168\) | \([2]\) | \(6635520\) | \(2.4814\) | |
| 389844.bt4 | 389844bt4 | \([0, 0, 0, 8648745, -1335558994]\) | \(3258571509326000/1920843121977\) | \(-42174275487103268151552\) | \([2]\) | \(19906560\) | \(3.0307\) |
Rank
sage: E.rank()
The elliptic curves in class 389844.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 389844.bt do not have complex multiplication.Modular form 389844.2.a.bt
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
