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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 238.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 238.d1 | 238c3 | \([1, -1, 1, -529, -4545]\) | \(16342588257633/8185058\) | \(8185058\) | \([2]\) | \(64\) | \(0.27913\) | |
| 238.d2 | 238c2 | \([1, -1, 1, -39, -37]\) | \(6403769793/2775556\) | \(2775556\) | \([2, 2]\) | \(32\) | \(-0.067444\) | |
| 238.d3 | 238c1 | \([1, -1, 1, -19, 35]\) | \(721734273/13328\) | \(13328\) | \([4]\) | \(16\) | \(-0.41402\) | \(\Gamma_0(N)\)-optimal |
| 238.d4 | 238c4 | \([1, -1, 1, 131, -377]\) | \(250404380127/196003234\) | \(-196003234\) | \([2]\) | \(64\) | \(0.27913\) |
Rank
sage: E.rank()
The elliptic curves in class 238.d have rank \(0\).
Complex multiplication
The elliptic curves in class 238.d do not have complex multiplication.Modular form 238.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
