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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 14651d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14651.j1 | 14651d1 | \([0, -1, 1, -2140679, -1204809558]\) | \(-9221261135586623488/121324931\) | \(-14273756807219\) | \([]\) | \(165888\) | \(2.0825\) | \(\Gamma_0(N)\)-optimal |
14651.j2 | 14651d2 | \([0, -1, 1, -2019649, -1347170777]\) | \(-7743965038771437568/2189290237869371\) | \(-257567807195093628779\) | \([]\) | \(497664\) | \(2.6318\) |
Rank
sage: E.rank()
The elliptic curves in class 14651d have rank \(0\).
Complex multiplication
The elliptic curves in class 14651d do not have complex multiplication.Modular form 14651.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.