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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 181944.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 181944.n1 | 181944bh3 | \([0, 0, 0, -13101051, 18251867590]\) | \(7080974546692/189\) | \(6637597214782464\) | \([2]\) | \(5308416\) | \(2.5497\) | |
| 181944.n2 | 181944bh4 | \([0, 0, 0, -1274691, -66436274]\) | \(6522128932/3720087\) | \(130647825978563238912\) | \([2]\) | \(5308416\) | \(2.5497\) | |
| 181944.n3 | 181944bh2 | \([0, 0, 0, -819831, 284442730]\) | \(6940769488/35721\) | \(313626468398471424\) | \([2, 2]\) | \(2654208\) | \(2.2031\) | |
| 181944.n4 | 181944bh1 | \([0, 0, 0, -23826, 9184201]\) | \(-2725888/64827\) | \(-35573372572974768\) | \([2]\) | \(1327104\) | \(1.8566\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 181944.n have rank \(2\).
Complex multiplication
The elliptic curves in class 181944.n do not have complex multiplication.Modular form 181944.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
