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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 126400.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126400.v1 | 126400bl3 | \([0, -1, 0, -8346433, 9283872737]\) | \(15698803397448457/20709376\) | \(84825604096000000\) | \([]\) | \(2488320\) | \(2.5243\) | |
126400.v2 | 126400bl2 | \([0, -1, 0, -130433, 5480737]\) | \(59914169497/31554496\) | \(129247215616000000\) | \([]\) | \(829440\) | \(1.9750\) | |
126400.v3 | 126400bl1 | \([0, -1, 0, -74433, -7791263]\) | \(11134383337/316\) | \(1294336000000\) | \([]\) | \(276480\) | \(1.4257\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126400.v have rank \(0\).
Complex multiplication
The elliptic curves in class 126400.v do not have complex multiplication.Modular form 126400.2.a.v
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.