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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 85800bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85800.v4 | 85800bs1 | \([0, -1, 0, 702617, 1588109512]\) | \(153440161062692864/4448256591796875\) | \(-1112064147949218750000\) | \([2]\) | \(3317760\) | \(2.7184\) | \(\Gamma_0(N)\)-optimal |
| 85800.v3 | 85800bs2 | \([0, -1, 0, -16875508, 25424047012]\) | \(132872256991684831696/7115280992015625\) | \(28461123968062500000000\) | \([2, 2]\) | \(6635520\) | \(3.0650\) | |
| 85800.v2 | 85800bs3 | \([0, -1, 0, -48563008, -97967077988]\) | \(791626776989285437924/198897898374693375\) | \(3182366373995094000000000\) | \([2]\) | \(13271040\) | \(3.4116\) | |
| 85800.v1 | 85800bs4 | \([0, -1, 0, -266438008, 1674033922012]\) | \(130735118598473711977924/407151596119125\) | \(6514425537906000000000\) | \([2]\) | \(13271040\) | \(3.4116\) |
Rank
sage: E.rank()
The elliptic curves in class 85800bs have rank \(1\).
Complex multiplication
The elliptic curves in class 85800bs do not have complex multiplication.Modular form 85800.2.a.bs
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 Cremona 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 Cremona labels.
