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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 39270b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39270.a3 | 39270b1 | \([1, 1, 0, -60133, -5700803]\) | \(24047703582479315929/46181520\) | \(46181520\) | \([2]\) | \(147456\) | \(1.1524\) | \(\Gamma_0(N)\)-optimal |
| 39270.a2 | 39270b2 | \([1, 1, 0, -60153, -5696847]\) | \(24071705871623664409/33323949836100\) | \(33323949836100\) | \([2, 2]\) | \(294912\) | \(1.4990\) | |
| 39270.a4 | 39270b3 | \([1, 1, 0, -43323, -8931573]\) | \(-8992800180983352889/29118607949103750\) | \(-29118607949103750\) | \([2]\) | \(589824\) | \(1.8456\) | |
| 39270.a1 | 39270b4 | \([1, 1, 0, -77303, -2208537]\) | \(51088309922344150009/27518869197465030\) | \(27518869197465030\) | \([2]\) | \(589824\) | \(1.8456\) |
Rank
sage: E.rank()
The elliptic curves in class 39270b have rank \(0\).
Complex multiplication
The elliptic curves in class 39270b do not have complex multiplication.Modular form 39270.2.a.b
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.
