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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 77616.fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.fe1 | 77616dh2 | \([0, 0, 0, -1618443099, -25060761630198]\) | \(144106117295241933/247808\) | \(806211378311759659008\) | \([2]\) | \(19869696\) | \(3.7005\) | |
77616.fe2 | 77616dh1 | \([0, 0, 0, -101120859, -391833187830]\) | \(-35148950502093/46137344\) | \(-150101900252953071058944\) | \([2]\) | \(9934848\) | \(3.3539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77616.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 77616.fe do not have complex multiplication.Modular form 77616.2.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.