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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 28830.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28830.bf1 | 28830bd6 | \([1, 1, 1, -295526740, 1955311431257]\) | \(3216206300355197383681/57660\) | \(51173462246460\) | \([2]\) | \(3932160\) | \(3.0988\) | |
| 28830.bf2 | 28830bd4 | \([1, 1, 1, -18470440, 30545903897]\) | \(785209010066844481/3324675600\) | \(2950661833130883600\) | \([2, 2]\) | \(1966080\) | \(2.7522\) | |
| 28830.bf3 | 28830bd5 | \([1, 1, 1, -18182140, 31545958937]\) | \(-749011598724977281/51173462246460\) | \(-45416636113247779219260\) | \([2]\) | \(3932160\) | \(3.0988\) | |
| 28830.bf4 | 28830bd3 | \([1, 1, 1, -3555720, -2013575655]\) | \(5601911201812801/1271193750000\) | \(1128189132389193750000\) | \([2]\) | \(1966080\) | \(2.7522\) | |
| 28830.bf5 | 28830bd2 | \([1, 1, 1, -1172440, 461222297]\) | \(200828550012481/12454560000\) | \(11053467845235360000\) | \([2, 2]\) | \(983040\) | \(2.4057\) | |
| 28830.bf6 | 28830bd1 | \([1, 1, 1, 57640, 30202265]\) | \(23862997439/457113600\) | \(-405690002635161600\) | \([4]\) | \(491520\) | \(2.0591\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28830.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 28830.bf do not have complex multiplication.Modular form 28830.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
