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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 479808eh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.eh1 | 479808eh1 | \([0, 0, 0, -595056, 176507800]\) | \(265327034368/297381\) | \(26117339984999424\) | \([2]\) | \(4423680\) | \(2.0642\) | \(\Gamma_0(N)\)-optimal |
479808.eh2 | 479808eh2 | \([0, 0, 0, -445116, 267611344]\) | \(-6940769488/18000297\) | \(-25293875618413559808\) | \([2]\) | \(8847360\) | \(2.4108\) |
Rank
sage: E.rank()
The elliptic curves in class 479808eh have rank \(0\).
Complex multiplication
The elliptic curves in class 479808eh do not have complex multiplication.Modular form 479808.2.a.eh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.