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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 100800s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.nx2 | 100800s1 | \([0, 0, 0, -600, 9000]\) | \(-55296/49\) | \(-21168000000\) | \([2]\) | \(65536\) | \(0.67842\) | \(\Gamma_0(N)\)-optimal |
100800.nx1 | 100800s2 | \([0, 0, 0, -11100, 450000]\) | \(21882096/7\) | \(48384000000\) | \([2]\) | \(131072\) | \(1.0250\) |
Rank
sage: E.rank()
The elliptic curves in class 100800s have rank \(0\).
Complex multiplication
The elliptic curves in class 100800s do not have complex multiplication.Modular form 100800.2.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.