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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 111090n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111090.o3 | 111090n1 | \([1, 1, 0, -6085362, 4809390516]\) | \(168351140229842809/29855318411520\) | \(4419658602427431041280\) | \([2]\) | \(8110080\) | \(2.8728\) | \(\Gamma_0(N)\)-optimal |
| 111090.o2 | 111090n2 | \([1, 1, 0, -28472642, -54010948956]\) | \(17244079743478944889/1469997007491600\) | \(217612313831358666032400\) | \([2, 2]\) | \(16220160\) | \(3.2194\) | |
| 111090.o4 | 111090n3 | \([1, 1, 0, 30658978, -248991552744]\) | \(21529289381199961031/193397385415972500\) | \(-28629753880329123837052500\) | \([4]\) | \(32440320\) | \(3.5660\) | |
| 111090.o1 | 111090n4 | \([1, 1, 0, -445800742, -3623084325776]\) | \(66187969564358252770489/550144842789780\) | \(81441180881150322414420\) | \([2]\) | \(32440320\) | \(3.5660\) |
Rank
sage: E.rank()
The elliptic curves in class 111090n have rank \(0\).
Complex multiplication
The elliptic curves in class 111090n do not have complex multiplication.Modular form 111090.2.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 Cremona 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 Cremona labels.
