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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 176400.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.fe1 | 176400jr2 | \([0, 0, 0, -316494675, -2167182816750]\) | \(68971442301/400\) | \(20333569192473600000000\) | \([2]\) | \(24772608\) | \(3.4708\) | |
| 176400.fe2 | 176400jr1 | \([0, 0, 0, -20142675, -32559360750]\) | \(17779581/1280\) | \(65067421415915520000000\) | \([2]\) | \(12386304\) | \(3.1242\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.fe do not have complex multiplication.Modular form 176400.2.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.
