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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 416025.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
416025.bx1 | 416025bx2 | \([1, -1, 0, -520032368067, -144342188729998534]\) | \(8000051600110940079507/144453125\) | \(280833552324243753662109375\) | \([2]\) | \(2384363520\) | \(5.0659\) | |
416025.bx2 | 416025bx1 | \([1, -1, 0, -32503071192, -2255187860857909]\) | \(1953326569433829507/262451171875\) | \(510235378496082401275634765625\) | \([2]\) | \(1192181760\) | \(4.7193\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 416025.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 416025.bx do not have complex multiplication.Modular form 416025.2.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 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.