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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 3450.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3450.y1 | 3450x2 | \([1, 0, 0, -788, 8442]\) | \(3463512697/3174\) | \(49593750\) | \([2]\) | \(2048\) | \(0.40017\) | |
3450.y2 | 3450x1 | \([1, 0, 0, -38, 192]\) | \(-389017/828\) | \(-12937500\) | \([2]\) | \(1024\) | \(0.053594\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3450.y have rank \(0\).
Complex multiplication
The elliptic curves in class 3450.y do not have complex multiplication.Modular form 3450.2.a.y
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 LMFDB 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 LMFDB labels.