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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 388080ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.ba3 | 388080ba1 | \([0, 0, 0, -509943, 140161462]\) | \(667932971344/3465\) | \(76077979971840\) | \([2]\) | \(2359296\) | \(1.8601\) | \(\Gamma_0(N)\)-optimal |
| 388080.ba2 | 388080ba2 | \([0, 0, 0, -518763, 135061738]\) | \(175798419556/12006225\) | \(1054440802409702400\) | \([2, 2]\) | \(4718592\) | \(2.2067\) | |
| 388080.ba4 | 388080ba3 | \([0, 0, 0, 451437, 581935858]\) | \(57925453822/866412855\) | \(-152184565264149411840\) | \([2]\) | \(9437184\) | \(2.5533\) | |
| 388080.ba1 | 388080ba4 | \([0, 0, 0, -1630083, -638194718]\) | \(2727138195938/576489375\) | \(101259791342519040000\) | \([2]\) | \(9437184\) | \(2.5533\) |
Rank
sage: E.rank()
The elliptic curves in class 388080ba have rank \(1\).
Complex multiplication
The elliptic curves in class 388080ba do not have complex multiplication.Modular form 388080.2.a.ba
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.
