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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 22218.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22218.m1 | 22218k4 | \([1, 0, 1, -802223486, 8703157266416]\) | \(385693937170561837203625/2159357734550274048\) | \(319662441903175833889308672\) | \([2]\) | \(15206400\) | \(3.9281\) | |
| 22218.m2 | 22218k2 | \([1, 0, 1, -59245631, -167237714446]\) | \(155355156733986861625/8291568305839392\) | \(1227449685359158285939488\) | \([2]\) | \(5068800\) | \(3.3788\) | |
| 22218.m3 | 22218k3 | \([1, 0, 1, -22181246, 286813513712]\) | \(-8152944444844179625/235342826399858688\) | \(-34839184525875750352453632\) | \([2]\) | \(7603200\) | \(3.5815\) | |
| 22218.m4 | 22218k1 | \([1, 0, 1, 2456929, -10439168974]\) | \(11079872671250375/324440155855872\) | \(-48028786899422567390208\) | \([2]\) | \(2534400\) | \(3.0322\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22218.m have rank \(1\).
Complex multiplication
The elliptic curves in class 22218.m do not have complex multiplication.Modular form 22218.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
