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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 111600ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111600.bb2 | 111600ee1 | \([0, 0, 0, -205635, 107949890]\) | \(-12882119799145/59982446592\) | \(-4477665645114163200\) | \([]\) | \(1382400\) | \(2.2635\) | \(\Gamma_0(N)\)-optimal |
| 111600.bb1 | 111600ee2 | \([0, 0, 0, -8551875, -15224818750]\) | \(-2372030262025/2061298872\) | \(-60107475107520000000000\) | \([]\) | \(6912000\) | \(3.0682\) |
Rank
sage: E.rank()
The elliptic curves in class 111600ee have rank \(1\).
Complex multiplication
The elliptic curves in class 111600ee do not have complex multiplication.Modular form 111600.2.a.ee
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
