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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 10890.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10890.f1 | 10890c4 | \([1, -1, 0, -26340, 436706]\) | \(57960603/31250\) | \(1089676098843750\) | \([2]\) | \(51840\) | \(1.5765\) | |
| 10890.f2 | 10890c2 | \([1, -1, 0, -15450, -735300]\) | \(8527173507/200\) | \(9566429400\) | \([2]\) | \(17280\) | \(1.0272\) | |
| 10890.f3 | 10890c1 | \([1, -1, 0, -930, -12204]\) | \(-1860867/320\) | \(-15306287040\) | \([2]\) | \(8640\) | \(0.68059\) | \(\Gamma_0(N)\)-optimal |
| 10890.f4 | 10890c3 | \([1, -1, 0, 6330, 51200]\) | \(804357/500\) | \(-17434817581500\) | \([2]\) | \(25920\) | \(1.2299\) |
Rank
sage: E.rank()
The elliptic curves in class 10890.f have rank \(0\).
Complex multiplication
The elliptic curves in class 10890.f do not have complex multiplication.Modular form 10890.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
