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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 46800.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.fe1 | 46800co2 | \([0, 0, 0, -608175, -182553750]\) | \(315978926832/169\) | \(13305708000000\) | \([2]\) | \(368640\) | \(1.8479\) | |
| 46800.fe2 | 46800co1 | \([0, 0, 0, -37800, -2885625]\) | \(-1213857792/28561\) | \(-140541540750000\) | \([2]\) | \(184320\) | \(1.5013\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.fe do not have complex multiplication.Modular form 46800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
