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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 9900p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9900.y2 | 9900p1 | \([0, 0, 0, -4800, 206125]\) | \(-67108864/61875\) | \(-11276718750000\) | \([2]\) | \(18432\) | \(1.2011\) | \(\Gamma_0(N)\)-optimal |
9900.y1 | 9900p2 | \([0, 0, 0, -89175, 10246750]\) | \(26894628304/9075\) | \(26462700000000\) | \([2]\) | \(36864\) | \(1.5477\) |
Rank
sage: E.rank()
The elliptic curves in class 9900p have rank \(0\).
Complex multiplication
The elliptic curves in class 9900p do not have complex multiplication.Modular form 9900.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.