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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 92575.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92575.w1 | 92575q4 | \([1, -1, 0, -1635767, -804656734]\) | \(209267191953/55223\) | \(127734154660109375\) | \([2]\) | \(1351680\) | \(2.2668\) | |
| 92575.w2 | 92575q2 | \([1, -1, 0, -114892, -9239109]\) | \(72511713/25921\) | \(59956848105765625\) | \([2, 2]\) | \(675840\) | \(1.9203\) | |
| 92575.w3 | 92575q1 | \([1, -1, 0, -48767, 4052016]\) | \(5545233/161\) | \(372402783265625\) | \([2]\) | \(337920\) | \(1.5737\) | \(\Gamma_0(N)\)-optimal |
| 92575.w4 | 92575q3 | \([1, -1, 0, 347983, -65246984]\) | \(2014698447/1958887\) | \(-4531024663992859375\) | \([2]\) | \(1351680\) | \(2.2668\) |
Rank
sage: E.rank()
The elliptic curves in class 92575.w have rank \(1\).
Complex multiplication
The elliptic curves in class 92575.w do not have complex multiplication.Modular form 92575.2.a.w
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.
