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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1904.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1904.b1 | 1904b2 | \([0, 1, 0, -2056, 6132]\) | \(234770924809/130960928\) | \(536415961088\) | \([2]\) | \(3840\) | \(0.94098\) | |
| 1904.b2 | 1904b1 | \([0, 1, 0, 504, 1012]\) | \(3449795831/2071552\) | \(-8485076992\) | \([2]\) | \(1920\) | \(0.59441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1904.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1904.b do not have complex multiplication.Modular form 1904.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
