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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 48510.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.cb1 | 48510dc4 | \([1, -1, 1, -1318915688, 18369733203371]\) | \(2958414657792917260183849/12401051653985258880\) | \(1063590096682949845318404480\) | \([2]\) | \(38535168\) | \(4.0406\) | |
| 48510.cb2 | 48510dc2 | \([1, -1, 1, -123629288, -30027523669]\) | \(2436531580079063806249/1405478914998681600\) | \(120542474686725640946073600\) | \([2, 2]\) | \(19267584\) | \(3.6940\) | |
| 48510.cb3 | 48510dc1 | \([1, -1, 1, -87502568, -314243655253]\) | \(863913648706111516969/2486234429521920\) | \(213234682916742962872320\) | \([2]\) | \(9633792\) | \(3.3475\) | \(\Gamma_0(N)\)-optimal |
| 48510.cb4 | 48510dc3 | \([1, -1, 1, 493629592, -240389349973]\) | \(155099895405729262880471/90047655797243760000\) | \(-7723038142872759786654960000\) | \([2]\) | \(38535168\) | \(4.0406\) |
Rank
sage: E.rank()
The elliptic curves in class 48510.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 48510.cb do not have complex multiplication.Modular form 48510.2.a.cb
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.
