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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 353925bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
353925.bx2 | 353925bx1 | \([0, 0, 1, 36300, 3452281]\) | \(7077888/10985\) | \(-8209939606171875\) | \([]\) | \(1555200\) | \(1.7390\) | \(\Gamma_0(N)\)-optimal |
353925.bx1 | 353925bx2 | \([0, 0, 1, -1143450, 472796156]\) | \(-303464448/1625\) | \(-885361830310546875\) | \([]\) | \(4665600\) | \(2.2883\) |
Rank
sage: E.rank()
The elliptic curves in class 353925bx have rank \(1\).
Complex multiplication
The elliptic curves in class 353925bx do not have complex multiplication.Modular form 353925.2.a.bx
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.