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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 600.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 600.d1 | 600c2 | \([0, -1, 0, -168, -468]\) | \(2060602/729\) | \(186624000\) | \([2]\) | \(192\) | \(0.28820\) | |
| 600.d2 | 600c1 | \([0, -1, 0, 32, -68]\) | \(27436/27\) | \(-3456000\) | \([2]\) | \(96\) | \(-0.058373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 600.d have rank \(0\).
Complex multiplication
The elliptic curves in class 600.d do not have complex multiplication.Modular form 600.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
