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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 338800y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338800.y2 | 338800y1 | \([0, 1, 0, 202, -3137]\) | \(1280/7\) | \(-4960370800\) | \([]\) | \(194400\) | \(0.54246\) | \(\Gamma_0(N)\)-optimal |
338800.y1 | 338800y2 | \([0, 1, 0, -11898, -504077]\) | \(-262885120/343\) | \(-243058169200\) | \([]\) | \(583200\) | \(1.0918\) |
Rank
sage: E.rank()
The elliptic curves in class 338800y have rank \(1\).
Complex multiplication
The elliptic curves in class 338800y do not have complex multiplication.Modular form 338800.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.