Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 28830.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28830.p1 | 28830m4 | \([1, 0, 1, -6370009, -6188532988]\) | \(32208729120020809/658986840\) | \(584853246230558040\) | \([2]\) | \(1105920\) | \(2.5287\) | |
28830.p2 | 28830m2 | \([1, 0, 1, -411809, -89719468]\) | \(8702409880009/1120910400\) | \(994812106071182400\) | \([2, 2]\) | \(552960\) | \(2.1821\) | |
28830.p3 | 28830m1 | \([1, 0, 1, -104289, 11516116]\) | \(141339344329/17141760\) | \(15213375098818560\) | \([2]\) | \(276480\) | \(1.8356\) | \(\Gamma_0(N)\)-optimal |
28830.p4 | 28830m3 | \([1, 0, 1, 626071, -468753244]\) | \(30579142915511/124675335000\) | \(-110649818742408135000\) | \([2]\) | \(1105920\) | \(2.5287\) |
Rank
sage: E.rank()
The elliptic curves in class 28830.p have rank \(1\).
Complex multiplication
The elliptic curves in class 28830.p do not have complex multiplication.Modular form 28830.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.