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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 126400q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126400.by3 | 126400q1 | \([0, 1, 0, -74433, 7791263]\) | \(11134383337/316\) | \(1294336000000\) | \([]\) | \(276480\) | \(1.4257\) | \(\Gamma_0(N)\)-optimal |
126400.by2 | 126400q2 | \([0, 1, 0, -130433, -5480737]\) | \(59914169497/31554496\) | \(129247215616000000\) | \([]\) | \(829440\) | \(1.9750\) | |
126400.by1 | 126400q3 | \([0, 1, 0, -8346433, -9283872737]\) | \(15698803397448457/20709376\) | \(84825604096000000\) | \([]\) | \(2488320\) | \(2.5243\) |
Rank
sage: E.rank()
The elliptic curves in class 126400q have rank \(0\).
Complex multiplication
The elliptic curves in class 126400q do not have complex multiplication.Modular form 126400.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.