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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 144150.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144150.br1 | 144150di4 | \([1, 0, 1, -15267191276, 726082642379198]\) | \(28379906689597370652529/1357352437500\) | \(18822738823368319335937500\) | \([2]\) | \(199065600\) | \(4.3270\) | |
144150.br2 | 144150di3 | \([1, 0, 1, -952615776, 11384516815198]\) | \(-6894246873502147249/47925198774000\) | \(-664590473821588860843750000\) | \([2]\) | \(99532800\) | \(3.9805\) | |
144150.br3 | 144150di2 | \([1, 0, 1, -204957776, 811579439198]\) | \(68663623745397169/19216056254400\) | \(266473760313798006975000000\) | \([2]\) | \(66355200\) | \(3.7777\) | |
144150.br4 | 144150di1 | \([1, 0, 1, 33370224, 83249071198]\) | \(296354077829711/387386634240\) | \(-5371985372784384960000000\) | \([2]\) | \(33177600\) | \(3.4312\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 144150.br have rank \(1\).
Complex multiplication
The elliptic curves in class 144150.br do not have complex multiplication.Modular form 144150.2.a.br
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.