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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 154560fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.fu4 | 154560fe1 | \([0, 1, 0, 18456319, 55473614175]\) | \(2652277923951208297919/6605028468326400000\) | \(-1731468582800955801600000\) | \([2]\) | \(29491200\) | \(3.3348\) | \(\Gamma_0(N)\)-optimal |
| 154560.fu3 | 154560fe2 | \([0, 1, 0, -154886401, 619565493599]\) | \(1567558142704512417614401/274462175610000000000\) | \(71948612563107840000000000\) | \([2, 2]\) | \(58982400\) | \(3.6813\) | |
| 154560.fu1 | 154560fe3 | \([0, 1, 0, -2362886401, 44206810293599]\) | \(5565604209893236690185614401/229307220930246900000\) | \(60111512123538643353600000\) | \([2]\) | \(117964800\) | \(4.0279\) | |
| 154560.fu2 | 154560fe4 | \([0, 1, 0, -720369921, -6863025539745]\) | \(157706830105239346386477121/13650704956054687500000\) | \(3578450400000000000000000000\) | \([2]\) | \(117964800\) | \(4.0279\) |
Rank
sage: E.rank()
The elliptic curves in class 154560fe have rank \(0\).
Complex multiplication
The elliptic curves in class 154560fe do not have complex multiplication.Modular form 154560.2.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.
