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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 33150s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33150.y2 | 33150s1 | \([1, 0, 1, -28451, 1688798]\) | \(162995025390625/15251079168\) | \(238298112000000\) | \([2]\) | \(147456\) | \(1.4971\) | \(\Gamma_0(N)\)-optimal |
33150.y1 | 33150s2 | \([1, 0, 1, -444451, 114008798]\) | \(621403856941038625/6310317312\) | \(98598708000000\) | \([2]\) | \(294912\) | \(1.8437\) |
Rank
sage: E.rank()
The elliptic curves in class 33150s have rank \(1\).
Complex multiplication
The elliptic curves in class 33150s do not have complex multiplication.Modular form 33150.2.a.s
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.