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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 11200cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11200.m2 | 11200cz1 | \([0, 1, 0, 167, 2463]\) | \(1280/7\) | \(-2800000000\) | \([]\) | \(5760\) | \(0.49481\) | \(\Gamma_0(N)\)-optimal |
11200.m1 | 11200cz2 | \([0, 1, 0, -9833, 372463]\) | \(-262885120/343\) | \(-137200000000\) | \([]\) | \(17280\) | \(1.0441\) |
Rank
sage: E.rank()
The elliptic curves in class 11200cz have rank \(1\).
Complex multiplication
The elliptic curves in class 11200cz do not have complex multiplication.Modular form 11200.2.a.cz
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.