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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 83490.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83490.m1 | 83490h6 | \([1, 1, 0, -165228565537, 25850839762935829]\) | \(281593741710042021666079895059441/1679852196000\) | \(2975960636197956000\) | \([2]\) | \(154828800\) | \(4.5861\) | |
| 83490.m2 | 83490h4 | \([1, 1, 0, -10326785537, 403916128451829]\) | \(68748475920312858086473939441/5309909096976000000\) | \(9406827869747899536000000\) | \([2, 2]\) | \(77414400\) | \(4.2395\) | |
| 83490.m3 | 83490h5 | \([1, 1, 0, -10305005537, 405704749967829]\) | \(-68314404928211802162172819441/604319586294334700196000\) | \(-1070589010615177875813925956000\) | \([2]\) | \(154828800\) | \(4.5861\) | |
| 83490.m4 | 83490h3 | \([1, 1, 0, -1117001217, -4062002637579]\) | \(87001860645030187942590961/46325683593750000000000\) | \(82068774353027343750000000000\) | \([2]\) | \(77414400\) | \(4.2395\) | |
| 83490.m5 | 83490h2 | \([1, 1, 0, -646785537, 6283024451829]\) | \(16890733200068263753939441/147476736000000000000\) | \(261264033904896000000000000\) | \([2, 2]\) | \(38707200\) | \(3.8929\) | |
| 83490.m6 | 83490h1 | \([1, 1, 0, -12397057, 231846496501]\) | \(-118938771937643854321/13039520710656000000\) | \(-23100306349690454016000000\) | \([2]\) | \(19353600\) | \(3.5463\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83490.m have rank \(1\).
Complex multiplication
The elliptic curves in class 83490.m do not have complex multiplication.Modular form 83490.2.a.m
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
