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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 55440.ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.ey1 | 55440ex4 | \([0, 0, 0, -430666347, 3427527178906]\) | \(2958414657792917260183849/12401051653985258880\) | \(37029341821973519251537920\) | \([2]\) | \(19267584\) | \(3.7608\) | |
| 55440.ey2 | 55440ex2 | \([0, 0, 0, -40368747, -5608570214]\) | \(2436531580079063806249/1405478914998681600\) | \(4196737552523423278694400\) | \([2, 2]\) | \(9633792\) | \(3.4142\) | |
| 55440.ey3 | 55440ex1 | \([0, 0, 0, -28572267, -58638466406]\) | \(863913648706111516969/2486234429521920\) | \(7423856226801580769280\) | \([2]\) | \(4816896\) | \(3.0677\) | \(\Gamma_0(N)\)-optimal |
| 55440.ey4 | 55440ex3 | \([0, 0, 0, 161185173, -44830963046]\) | \(155099895405729262880471/90047655797243760000\) | \(-268880859448077111459840000\) | \([4]\) | \(19267584\) | \(3.7608\) |
Rank
sage: E.rank()
The elliptic curves in class 55440.ey have rank \(0\).
Complex multiplication
The elliptic curves in class 55440.ey do not have complex multiplication.Modular form 55440.2.a.ey
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.
