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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5520.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.i1 | 5520u3 | \([0, -1, 0, -1766400, -903022848]\) | \(148809678420065817601/20700\) | \(84787200\) | \([2]\) | \(36864\) | \(1.8462\) | |
| 5520.i2 | 5520u5 | \([0, -1, 0, -413280, 87734400]\) | \(1905890658841300321/293666194803750\) | \(1202856733916160000\) | \([4]\) | \(73728\) | \(2.1927\) | |
| 5520.i3 | 5520u4 | \([0, -1, 0, -113280, -13305600]\) | \(39248884582600321/3935264062500\) | \(16118841600000000\) | \([2, 4]\) | \(36864\) | \(1.8462\) | |
| 5520.i4 | 5520u2 | \([0, -1, 0, -110400, -14082048]\) | \(36330796409313601/428490000\) | \(1755095040000\) | \([2, 2]\) | \(18432\) | \(1.4996\) | |
| 5520.i5 | 5520u1 | \([0, -1, 0, -6720, -230400]\) | \(-8194759433281/965779200\) | \(-3955831603200\) | \([2]\) | \(9216\) | \(1.1530\) | \(\Gamma_0(N)\)-optimal |
| 5520.i6 | 5520u6 | \([0, -1, 0, 140640, -64699008]\) | \(75108181893694559/484313964843750\) | \(-1983750000000000000\) | \([4]\) | \(73728\) | \(2.1927\) |
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.
