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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 13200by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13200.y1 | 13200by1 | \([0, -1, 0, -9333, -360963]\) | \(-56197120/3267\) | \(-5227200000000\) | \([]\) | \(25920\) | \(1.1967\) | \(\Gamma_0(N)\)-optimal |
13200.y2 | 13200by2 | \([0, -1, 0, 50667, -660963]\) | \(8990228480/5314683\) | \(-8503492800000000\) | \([]\) | \(77760\) | \(1.7460\) |
Rank
sage: E.rank()
The elliptic curves in class 13200by have rank \(0\).
Complex multiplication
The elliptic curves in class 13200by do not have complex multiplication.Modular form 13200.2.a.by
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.