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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1155.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1155.d1 | 1155a3 | \([1, 1, 1, -881, 9698]\) | \(75627935783569/396165\) | \(396165\) | \([2]\) | \(384\) | \(0.27015\) | |
| 1155.d2 | 1155a2 | \([1, 1, 1, -56, 128]\) | \(19443408769/1334025\) | \(1334025\) | \([2, 2]\) | \(192\) | \(-0.076428\) | |
| 1155.d3 | 1155a1 | \([1, 1, 1, -11, -16]\) | \(148035889/31185\) | \(31185\) | \([2]\) | \(96\) | \(-0.42300\) | \(\Gamma_0(N)\)-optimal |
| 1155.d4 | 1155a4 | \([1, 1, 1, 49, 674]\) | \(12994449551/192163125\) | \(-192163125\) | \([2]\) | \(384\) | \(0.27015\) |
Rank
sage: E.rank()
The elliptic curves in class 1155.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1155.d do not have complex multiplication.Modular form 1155.2.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.
