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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 330330.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 330330.j1 | 330330j1 | \([1, 1, 0, -11013, -365427]\) | \(83396175409/16511040\) | \(29250314533440\) | \([2]\) | \(1075200\) | \(1.3003\) | \(\Gamma_0(N)\)-optimal |
| 330330.j2 | 330330j2 | \([1, 1, 0, 22867, -2133963]\) | \(746389464911/1552332600\) | \(-2750051893188600\) | \([2]\) | \(2150400\) | \(1.6469\) |
Rank
sage: E.rank()
The elliptic curves in class 330330.j have rank \(1\).
Complex multiplication
The elliptic curves in class 330330.j do not have complex multiplication.Modular form 330330.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
