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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 137280ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137280.gb2 | 137280ee1 | \([0, 1, 0, -116865, -15624225]\) | \(-673350049820449/10617750000\) | \(-2783379456000000\) | \([2]\) | \(884736\) | \(1.7649\) | \(\Gamma_0(N)\)-optimal |
| 137280.gb1 | 137280ee2 | \([0, 1, 0, -1876865, -990312225]\) | \(2789222297765780449/677605500\) | \(177630216192000\) | \([2]\) | \(1769472\) | \(2.1115\) |
Rank
sage: E.rank()
The elliptic curves in class 137280ee have rank \(0\).
Complex multiplication
The elliptic curves in class 137280ee do not have complex multiplication.Modular form 137280.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
