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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 361920bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.bd4 | 361920bd1 | \([0, -1, 0, -1812161, 269699265]\) | \(2510581756496128561/1333551278592000\) | \(349582466375221248000\) | \([2]\) | \(13271040\) | \(2.6334\) | \(\Gamma_0(N)\)-optimal |
| 361920.bd2 | 361920bd2 | \([0, -1, 0, -16742081, -26159245119]\) | \(1979758117698975186481/17510434929000000\) | \(4590255454027776000000\) | \([2, 2]\) | \(26542080\) | \(2.9799\) | |
| 361920.bd3 | 361920bd3 | \([0, -1, 0, -5060801, -61999748415]\) | \(-54681655838565466801/6303365630859375000\) | \(-1652389479936000000000000\) | \([2]\) | \(53084160\) | \(3.3265\) | |
| 361920.bd1 | 361920bd4 | \([0, -1, 0, -267302081, -1682010061119]\) | \(8057323694463985606146481/638717154543000\) | \(167435869760520192000\) | \([2]\) | \(53084160\) | \(3.3265\) |
Rank
sage: E.rank()
The elliptic curves in class 361920bd have rank \(0\).
Complex multiplication
The elliptic curves in class 361920bd do not have complex multiplication.Modular form 361920.2.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 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.
