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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 4800bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.cg4 | 4800bd1 | \([0, 1, 0, -4833, -177537]\) | \(-24389/12\) | \(-6144000000000\) | \([2]\) | \(7680\) | \(1.1592\) | \(\Gamma_0(N)\)-optimal |
| 4800.cg2 | 4800bd2 | \([0, 1, 0, -84833, -9537537]\) | \(131872229/18\) | \(9216000000000\) | \([2]\) | \(15360\) | \(1.5057\) | |
| 4800.cg3 | 4800bd3 | \([0, 1, 0, -44833, 17542463]\) | \(-19465109/248832\) | \(-127401984000000000\) | \([2]\) | \(38400\) | \(1.9639\) | |
| 4800.cg1 | 4800bd4 | \([0, 1, 0, -1324833, 584582463]\) | \(502270291349/1889568\) | \(967458816000000000\) | \([2]\) | \(76800\) | \(2.3105\) |
Rank
sage: E.rank()
The elliptic curves in class 4800bd have rank \(1\).
Complex multiplication
The elliptic curves in class 4800bd do not have complex multiplication.Modular form 4800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
