Show commands:
SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 144150.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 144150.eb1 | 144150n3 | \([1, 0, 0, -36362338, 80758970042]\) | \(383432500775449/18701300250\) | \(259335512677519066406250\) | \([2]\) | \(26542080\) | \(3.2523\) | |
| 144150.eb2 | 144150n2 | \([1, 0, 0, -6331088, -4499748708]\) | \(2023804595449/540562500\) | \(7496112633758789062500\) | \([2, 2]\) | \(13271040\) | \(2.9057\) | |
| 144150.eb3 | 144150n1 | \([1, 0, 0, -5850588, -5446814208]\) | \(1597099875769/186000\) | \(2579307572906250000\) | \([2]\) | \(6635520\) | \(2.5592\) | \(\Gamma_0(N)\)-optimal |
| 144150.eb4 | 144150n4 | \([1, 0, 0, 16012162, -29144353458]\) | \(32740359775271/45410156250\) | \(-629713762916564941406250\) | \([2]\) | \(26542080\) | \(3.2523\) |
Rank
sage: E.rank()
The elliptic curves in class 144150.eb have rank \(0\).
Complex multiplication
The elliptic curves in class 144150.eb do not have complex multiplication.Modular form 144150.2.a.eb
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.
