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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 119952.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.bt1 | 119952gp4 | \([0, 0, 0, -35837571, -82576372606]\) | \(14489843500598257/6246072\) | \(2194232798931812352\) | \([2]\) | \(7077888\) | \(2.8620\) | |
| 119952.bt2 | 119952gp3 | \([0, 0, 0, -4791171, 2133673346]\) | \(34623662831857/14438442312\) | \(5072196363806768136192\) | \([2]\) | \(7077888\) | \(2.8620\) | |
| 119952.bt3 | 119952gp2 | \([0, 0, 0, -2251011, -1276745470]\) | \(3590714269297/73410624\) | \(25789007710902288384\) | \([2, 2]\) | \(3538944\) | \(2.5154\) | |
| 119952.bt4 | 119952gp1 | \([0, 0, 0, 6909, -59726590]\) | \(103823/4386816\) | \(-1541079825861574656\) | \([2]\) | \(1769472\) | \(2.1688\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.bt do not have complex multiplication.Modular form 119952.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
