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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 165048i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 165048.a1 | 165048i1 | \([0, -1, 0, -344555, -73020084]\) | \(1909913257984/129730653\) | \(307276680758488272\) | \([2]\) | \(2956800\) | \(2.1041\) | \(\Gamma_0(N)\)-optimal |
| 165048.a2 | 165048i2 | \([0, -1, 0, 298180, -314688444]\) | \(77366117936/1172914587\) | \(-44450164123548887808\) | \([2]\) | \(5913600\) | \(2.4507\) |
Rank
sage: E.rank()
The elliptic curves in class 165048i have rank \(1\).
Complex multiplication
The elliptic curves in class 165048i do not have complex multiplication.Modular form 165048.2.a.i
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.
