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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 360.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360.d1 | 360c2 | \([0, 0, 0, -1107, 14094]\) | \(3721734/25\) | \(1007769600\) | \([2]\) | \(192\) | \(0.56230\) | |
| 360.d2 | 360c1 | \([0, 0, 0, -27, 486]\) | \(-108/5\) | \(-100776960\) | \([2]\) | \(96\) | \(0.21572\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 360.d have rank \(0\).
Complex multiplication
The elliptic curves in class 360.d do not have complex multiplication.Modular form 360.2.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.
