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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 100920i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100920.v5 | 100920i1 | \([0, -1, 0, -12895, 567052]\) | \(24918016/45\) | \(428272791120\) | \([2]\) | \(200704\) | \(1.1239\) | \(\Gamma_0(N)\)-optimal |
| 100920.v4 | 100920i2 | \([0, -1, 0, -17100, 170100]\) | \(3631696/2025\) | \(308356409606400\) | \([2, 2]\) | \(401408\) | \(1.4705\) | |
| 100920.v6 | 100920i3 | \([0, -1, 0, 67000, 1280220]\) | \(54607676/32805\) | \(-19981495342494720\) | \([2]\) | \(802816\) | \(1.8171\) | |
| 100920.v2 | 100920i4 | \([0, -1, 0, -168480, -26412228]\) | \(868327204/5625\) | \(3426182328960000\) | \([2, 2]\) | \(802816\) | \(1.8171\) | |
| 100920.v3 | 100920i5 | \([0, -1, 0, -67560, -57858900]\) | \(-27995042/1171875\) | \(-1427575970400000000\) | \([2]\) | \(1605632\) | \(2.1636\) | |
| 100920.v1 | 100920i6 | \([0, -1, 0, -2691480, -1698656628]\) | \(1770025017602/75\) | \(91364862105600\) | \([2]\) | \(1605632\) | \(2.1636\) |
Rank
sage: E.rank()
The elliptic curves in class 100920i have rank \(0\).
Complex multiplication
The elliptic curves in class 100920i do not have complex multiplication.Modular form 100920.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
