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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 182.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 182.d1 | 182b3 | \([1, 0, 0, -15663, -755809]\) | \(-424962187484640625/182\) | \(-182\) | \([]\) | \(108\) | \(0.68046\) | |
| 182.d2 | 182b2 | \([1, 0, 0, -193, -1055]\) | \(-795309684625/6028568\) | \(-6028568\) | \([3]\) | \(36\) | \(0.13115\) | |
| 182.d3 | 182b1 | \([1, 0, 0, 7, -7]\) | \(37595375/46592\) | \(-46592\) | \([3]\) | \(12\) | \(-0.41816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182.d have rank \(0\).
Complex multiplication
The elliptic curves in class 182.d do not have complex multiplication.Modular form 182.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
