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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 255024.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 255024.bd1 | 255024bd4 | \([0, 0, 0, -992451, -380536126]\) | \(36204575259448513/1527466248\) | \(4560989777068032\) | \([2]\) | \(2654208\) | \(2.0848\) | |
| 255024.bd2 | 255024bd2 | \([0, 0, 0, -65091, -5326270]\) | \(10214075575873/1806590016\) | \(5394448882335744\) | \([2, 2]\) | \(1327104\) | \(1.7382\) | |
| 255024.bd3 | 255024bd1 | \([0, 0, 0, -19011, 931394]\) | \(254478514753/21762048\) | \(64981127135232\) | \([2]\) | \(663552\) | \(1.3916\) | \(\Gamma_0(N)\)-optimal |
| 255024.bd4 | 255024bd3 | \([0, 0, 0, 124989, -30606910]\) | \(72318867421247/177381135624\) | \(-529657232875094016\) | \([2]\) | \(2654208\) | \(2.0848\) |
Rank
sage: E.rank()
The elliptic curves in class 255024.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 255024.bd do not have complex multiplication.Modular form 255024.2.a.bd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
