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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 433251.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433251.q1 | 433251q1 | \([0, 0, 1, -207995394, 1154592401760]\) | \(-9221261135586623488/121324931\) | \(-13093163689449072411\) | \([]\) | \(54743040\) | \(3.2266\) | \(\Gamma_0(N)\)-optimal |
433251.q2 | 433251q2 | \([0, 0, 1, -196235724, 1290900531627]\) | \(-7743965038771437568/2189290237869371\) | \(-236264180922028061552892051\) | \([]\) | \(164229120\) | \(3.7759\) |
Rank
sage: E.rank()
The elliptic curves in class 433251.q have rank \(0\).
Complex multiplication
The elliptic curves in class 433251.q do not have complex multiplication.Modular form 433251.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.