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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 130050y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 130050.dw3 | 130050y1 | \([1, -1, 1, -6568880, -5657078253]\) | \(114013572049/15667200\) | \(4307571253684800000000\) | \([2]\) | \(10616832\) | \(2.8780\) | \(\Gamma_0(N)\)-optimal |
| 130050.dw2 | 130050y2 | \([1, -1, 1, -27376880, 49442505747]\) | \(8253429989329/936360000\) | \(257444688208505625000000\) | \([2, 2]\) | \(21233664\) | \(3.2246\) | |
| 130050.dw1 | 130050y3 | \([1, -1, 1, -425329880, 3376329585747]\) | \(30949975477232209/478125000\) | \(131456642263330078125000\) | \([2]\) | \(42467328\) | \(3.5712\) | |
| 130050.dw4 | 130050y4 | \([1, -1, 1, 37648120, 248679105747]\) | \(21464092074671/109596256200\) | \(-30132613531364540878125000\) | \([2]\) | \(42467328\) | \(3.5712\) |
Rank
sage: E.rank()
The elliptic curves in class 130050y have rank \(1\).
Complex multiplication
The elliptic curves in class 130050y do not have complex multiplication.Modular form 130050.2.a.y
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.
