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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 324870.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 324870.cy1 | 324870cy3 | \([1, 0, 1, -19075960731133, 32068431719409689468]\) | \(6525213578865970265696405437575208534969/767130688571676495117187500\) | \(90252158379769167974041992187500\) | \([4]\) | \(12173967360\) | \(5.9969\) | |
| 324870.cy2 | 324870cy2 | \([1, 0, 1, -1192345656353, 500982580564994756]\) | \(1593463037319346477727119157097168889/546221162511858816329870250000\) | \(64262373548357677882392905042250000\) | \([2, 2]\) | \(6086983680\) | \(5.6504\) | |
| 324870.cy3 | 324870cy4 | \([1, 0, 1, -1025578198853, 646099819783463756]\) | \(-1014009007595272988562623757184248889/946022301497270062664245652323500\) | \(-111298577748852325602385836750207451500\) | \([2]\) | \(12173967360\) | \(5.9969\) | |
| 324870.cy4 | 324870cy1 | \([1, 0, 1, -85042680273, 5473800114193828]\) | \(578157667940817624228325381788409/224561259415530338819315616000\) | \(26419407608977728831753662906784000\) | \([2]\) | \(3043491840\) | \(5.3038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 324870.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 324870.cy do not have complex multiplication.Modular form 324870.2.a.cy
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.
