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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 364650.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 364650.fe1 | 364650fe4 | \([1, 0, 0, -59205976250213, -175237849506168035583]\) | \(1468927380112885544150359654167819387617929/1050576937035228872669899013898240000\) | \(16415264641175451135467172092160000000000\) | \([2]\) | \(60162048000\) | \(6.6520\) | |
| 364650.fe2 | 364650fe2 | \([1, 0, 0, -4456595642213, -1538486355950819583]\) | \(626488898963524376216729490312431616649/297110313239417758856828453231001600\) | \(4642348644365902482137944581734400000000\) | \([2, 2]\) | \(30081024000\) | \(6.3054\) | |
| 364650.fe3 | 364650fe1 | \([1, 0, 0, -2309111994213, 1334028573803292417]\) | \(87144238160389744736714936955702559369/1227407131985056007698981501009920\) | \(19178236437266500120296585953280000000\) | \([2]\) | \(15040512000\) | \(5.9588\) | \(\Gamma_0(N)\)-optimal |
| 364650.fe4 | 364650fe3 | \([1, 0, 0, 15933046597787, -11680070120062179583]\) | \(28628603581889875812685935412788452965751/20339331585138070705332692997122949120\) | \(-317802056017782354770823328080046080000000\) | \([2]\) | \(60162048000\) | \(6.6520\) |
Rank
sage: E.rank()
The elliptic curves in class 364650.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.fe do not have complex multiplication.Modular form 364650.2.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 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.
