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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4032.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4032.b1 | 4032k1 | \([0, 0, 0, -3387, 59740]\) | \(92100460096/20253807\) | \(944961619392\) | \([2]\) | \(7680\) | \(1.0114\) | \(\Gamma_0(N)\)-optimal |
| 4032.b2 | 4032k2 | \([0, 0, 0, 7548, 365920]\) | \(15926924096/28588707\) | \(-85365421682688\) | \([2]\) | \(15360\) | \(1.3580\) |
Rank
sage: E.rank()
The elliptic curves in class 4032.b have rank \(0\).
Complex multiplication
The elliptic curves in class 4032.b do not have complex multiplication.Modular form 4032.2.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.
