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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 33462.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33462.bf1 | 33462bg4 | \([1, -1, 0, -7596666, 8060920492]\) | \(13778603383488553/13703976\) | \(48220780050893736\) | \([2]\) | \(1032192\) | \(2.4939\) | |
| 33462.bf2 | 33462bg3 | \([1, -1, 0, -1147626, -299055236]\) | \(47504791830313/16490207448\) | \(58024814575245731928\) | \([2]\) | \(1032192\) | \(2.4939\) | |
| 33462.bf3 | 33462bg2 | \([1, -1, 0, -478386, 124038292]\) | \(3440899317673/106007616\) | \(373013637418483776\) | \([2, 2]\) | \(516096\) | \(2.1473\) | |
| 33462.bf4 | 33462bg1 | \([1, -1, 0, 8334, 6544084]\) | \(18191447/5271552\) | \(-18549240710787072\) | \([2]\) | \(258048\) | \(1.8008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33462.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 33462.bf do not have complex multiplication.Modular form 33462.2.a.bf
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.
