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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 74970.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74970.y1 | 74970bd4 | \([1, -1, 0, -2884590, -1884961044]\) | \(30949975477232209/478125000\) | \(41006926603125000\) | \([2]\) | \(1769472\) | \(2.3228\) | |
74970.y2 | 74970bd2 | \([1, -1, 0, -185670, -27564300]\) | \(8253429989329/936360000\) | \(80307965059560000\) | \([2, 2]\) | \(884736\) | \(1.9762\) | |
74970.y3 | 74970bd1 | \([1, -1, 0, -44550, 3171636]\) | \(114013572049/15667200\) | \(1343714970931200\) | \([2]\) | \(442368\) | \(1.6296\) | \(\Gamma_0(N)\)-optimal |
74970.y4 | 74970bd3 | \([1, -1, 0, 255330, -138960900]\) | \(21464092074671/109596256200\) | \(-9399645770396200200\) | \([2]\) | \(1769472\) | \(2.3228\) |
Rank
sage: E.rank()
The elliptic curves in class 74970.y have rank \(0\).
Complex multiplication
The elliptic curves in class 74970.y do not have complex multiplication.Modular form 74970.2.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 LMFDB 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 LMFDB labels.