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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 66424.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66424.i1 | 66424h4 | \([0, 0, 0, -220571, -35433594]\) | \(24634706148/2997383\) | \(144398872503729152\) | \([2]\) | \(472320\) | \(2.0230\) | |
| 66424.i2 | 66424h2 | \([0, 0, 0, -54511, 4321170]\) | \(1487354832/190969\) | \(2299982041264384\) | \([2, 2]\) | \(236160\) | \(1.6764\) | |
| 66424.i3 | 66424h1 | \([0, 0, 0, -52706, 4657261]\) | \(21511084032/437\) | \(328944799952\) | \([4]\) | \(118080\) | \(1.3299\) | \(\Gamma_0(N)\)-optimal |
| 66424.i4 | 66424h3 | \([0, 0, 0, 82669, 22566110]\) | \(1296970812/5316979\) | \(-256145368385022976\) | \([2]\) | \(472320\) | \(2.0230\) |
Rank
sage: E.rank()
The elliptic curves in class 66424.i have rank \(1\).
Complex multiplication
The elliptic curves in class 66424.i do not have complex multiplication.Modular form 66424.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
