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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 57330.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.q1 | 57330s6 | \([1, -1, 0, -233309295, -1370947399529]\) | \(16375858190544687071329/9025573730468750\) | \(774088448661804199218750\) | \([2]\) | \(11943936\) | \(3.5318\) | |
57330.q2 | 57330s5 | \([1, -1, 0, -233278425, -1371328514375]\) | \(16369358802802724130049/4976562500\) | \(426820461539062500\) | \([2]\) | \(5971968\) | \(3.1852\) | |
57330.q3 | 57330s4 | \([1, -1, 0, -8977005, 8131701325]\) | \(932829715460155969/206949435875000\) | \(17749250358136990875000\) | \([2]\) | \(3981312\) | \(2.9825\) | |
57330.q4 | 57330s2 | \([1, -1, 0, -8430165, 9423220981]\) | \(772531501373731009/15142400\) | \(1298704910630400\) | \([2]\) | \(1327104\) | \(2.4332\) | |
57330.q5 | 57330s3 | \([1, -1, 0, -2926485, -1816563659]\) | \(32318182904349889/2067798824000\) | \(177347084142841704000\) | \([2]\) | \(1990656\) | \(2.6359\) | |
57330.q6 | 57330s1 | \([1, -1, 0, -527445, 147008245]\) | \(189208196468929/834928640\) | \(71608590764605440\) | \([2]\) | \(663552\) | \(2.0866\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57330.q have rank \(1\).
Complex multiplication
The elliptic curves in class 57330.q do not have complex multiplication.Modular form 57330.2.a.q
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 6 & 18 \\ 2 & 1 & 6 & 18 & 3 & 9 \\ 3 & 6 & 1 & 3 & 2 & 6 \\ 9 & 18 & 3 & 1 & 6 & 2 \\ 6 & 3 & 2 & 6 & 1 & 3 \\ 18 & 9 & 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.