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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 54450bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54450.y1 | 54450bj1 | \([1, -1, 0, -315565542, 2105479112116]\) | \(129392980254539/3583180800\) | \(96238854055889740800000000\) | \([2]\) | \(22708224\) | \(3.7652\) | \(\Gamma_0(N)\)-optimal |
54450.y2 | 54450bj2 | \([1, -1, 0, 67762458, 6894395816116]\) | \(1281177907381/765275040000\) | \(-20554138068381920227500000000\) | \([2]\) | \(45416448\) | \(4.1118\) |
Rank
sage: E.rank()
The elliptic curves in class 54450bj have rank \(0\).
Complex multiplication
The elliptic curves in class 54450bj do not have complex multiplication.Modular form 54450.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.