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SageMath
sage: E = EllipticCurve("i1")
sage: E.isogeny_class()
Elliptic curves in class 5520.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 5520.i1 | 5520u3 | [0, -1, 0, -1766400, -903022848] | [2] | 36864 | |
| 5520.i2 | 5520u5 | [0, -1, 0, -413280, 87734400] | [4] | 73728 | |
| 5520.i3 | 5520u4 | [0, -1, 0, -113280, -13305600] | [2, 4] | 36864 | |
| 5520.i4 | 5520u2 | [0, -1, 0, -110400, -14082048] | [2, 2] | 18432 | |
| 5520.i5 | 5520u1 | [0, -1, 0, -6720, -230400] | [2] | 9216 | \(\Gamma_0(N)\)-optimal |
| 5520.i6 | 5520u6 | [0, -1, 0, 140640, -64699008] | [4] | 73728 |
Rank
sage: E.rank()
The elliptic curves in class 5520.i have rank \(0\).
Complex multiplication
The elliptic curves in class 5520.i do not have complex multiplication.Modular form 5520.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
