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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 356928fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 356928.fe3 | 356928fe1 | \([0, 1, 0, -22364, -1294734]\) | \(4004529472/99\) | \(30582661824\) | \([2]\) | \(491520\) | \(1.1211\) | \(\Gamma_0(N)\)-optimal |
| 356928.fe2 | 356928fe2 | \([0, 1, 0, -23209, -1192489]\) | \(69934528/9801\) | \(193771745316864\) | \([2, 2]\) | \(983040\) | \(1.4677\) | |
| 356928.fe1 | 356928fe3 | \([0, 1, 0, -97569, 10511775]\) | \(649461896/72171\) | \(11414917360484352\) | \([2]\) | \(1966080\) | \(1.8143\) | |
| 356928.fe4 | 356928fe4 | \([0, 1, 0, 37631, -6339553]\) | \(37259704/131769\) | \(-20841227718524928\) | \([2]\) | \(1966080\) | \(1.8143\) |
Rank
sage: E.rank()
The elliptic curves in class 356928fe have rank \(1\).
Complex multiplication
The elliptic curves in class 356928fe do not have complex multiplication.Modular form 356928.2.a.fe
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.
