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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 360640bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360640.bt2 | 360640bt1 | \([0, 1, 0, -28600385, -56430037217]\) | \(83890194895342081/3958384640000\) | \(122080459361185955840000\) | \([2]\) | \(41287680\) | \(3.1906\) | \(\Gamma_0(N)\)-optimal |
360640.bt1 | 360640bt2 | \([0, 1, 0, -78776385, 195644151583]\) | \(1753007192038126081/478174101507200\) | \(14747357640974813836083200\) | \([2]\) | \(82575360\) | \(3.5372\) |
Rank
sage: E.rank()
The elliptic curves in class 360640bt have rank \(0\).
Complex multiplication
The elliptic curves in class 360640bt do not have complex multiplication.Modular form 360640.2.a.bt
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.