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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 235200.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.d1 | 235200d2 | \([0, -1, 0, -237813, 44717037]\) | \(-30866268160/3\) | \(-144567091200\) | \([]\) | \(1306368\) | \(1.5747\) | |
| 235200.d2 | 235200d1 | \([0, -1, 0, -2613, 76077]\) | \(-40960/27\) | \(-1301103820800\) | \([]\) | \(435456\) | \(1.0254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.d have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.d do not have complex multiplication.Modular form 235200.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
