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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 73920.dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.dt1 | 73920gb4 | \([0, -1, 0, -191407265, -1015499806143]\) | \(2958414657792917260183849/12401051653985258880\) | \(3250861284782311703838720\) | \([2]\) | \(19267584\) | \(3.5581\) | |
| 73920.dt2 | 73920gb2 | \([0, -1, 0, -17941665, 1667779137]\) | \(2436531580079063806249/1405478914998681600\) | \(368437864693414389350400\) | \([2, 2]\) | \(9633792\) | \(3.2115\) | |
| 73920.dt3 | 73920gb1 | \([0, -1, 0, -12698785, 17378593345]\) | \(863913648706111516969/2486234429521920\) | \(651751438292594196480\) | \([2]\) | \(4816896\) | \(2.8649\) | \(\Gamma_0(N)\)-optimal |
| 73920.dt4 | 73920gb3 | \([0, -1, 0, 71637855, 13259369025]\) | \(155099895405729262880471/90047655797243760000\) | \(-23605452681312668221440000\) | \([4]\) | \(19267584\) | \(3.5581\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.dt do not have complex multiplication.Modular form 73920.2.a.dt
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.
