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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 479808.eg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.eg1 | 479808eg1 | \([0, 0, 0, -595056, -176507800]\) | \(265327034368/297381\) | \(26117339984999424\) | \([2]\) | \(4423680\) | \(2.0642\) | \(\Gamma_0(N)\)-optimal |
479808.eg2 | 479808eg2 | \([0, 0, 0, -445116, -267611344]\) | \(-6940769488/18000297\) | \(-25293875618413559808\) | \([2]\) | \(8847360\) | \(2.4108\) |
Rank
sage: E.rank()
The elliptic curves in class 479808.eg have rank \(1\).
Complex multiplication
The elliptic curves in class 479808.eg do not have complex multiplication.Modular form 479808.2.a.eg
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.