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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 28158r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28158.u4 | 28158r1 | \([1, 0, 0, -7047, -4754295]\) | \(-822656953/207028224\) | \(-9739825189945344\) | \([2]\) | \(241920\) | \(1.7472\) | \(\Gamma_0(N)\)-optimal |
| 28158.u3 | 28158r2 | \([1, 0, 0, -469127, -122584695]\) | \(242702053576633/2554695936\) | \(120187920996239616\) | \([2, 2]\) | \(483840\) | \(2.0937\) | |
| 28158.u2 | 28158r3 | \([1, 0, 0, -844567, 101252633]\) | \(1416134368422073/725251155408\) | \(34120079552437274448\) | \([2]\) | \(967680\) | \(2.4403\) | |
| 28158.u1 | 28158r4 | \([1, 0, 0, -7486967, -7885719303]\) | \(986551739719628473/111045168\) | \(5224217759353008\) | \([2]\) | \(967680\) | \(2.4403\) |
Rank
sage: E.rank()
The elliptic curves in class 28158r have rank \(0\).
Complex multiplication
The elliptic curves in class 28158r do not have complex multiplication.Modular form 28158.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
