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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 111090.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111090.p1 | 111090o4 | \([1, 1, 0, -197592, -33889086]\) | \(5763259856089/5670\) | \(839363490630\) | \([2]\) | \(720896\) | \(1.5813\) | |
| 111090.p2 | 111090o2 | \([1, 1, 0, -12442, -525056]\) | \(1439069689/44100\) | \(6528382704900\) | \([2, 2]\) | \(360448\) | \(1.2348\) | |
| 111090.p3 | 111090o1 | \([1, 1, 0, -1862, 18756]\) | \(4826809/1680\) | \(248700293520\) | \([2]\) | \(180224\) | \(0.88818\) | \(\Gamma_0(N)\)-optimal |
| 111090.p4 | 111090o3 | \([1, 1, 0, 3428, -1753394]\) | \(30080231/9003750\) | \(-1332878135583750\) | \([2]\) | \(720896\) | \(1.5813\) |
Rank
sage: E.rank()
The elliptic curves in class 111090.p have rank \(0\).
Complex multiplication
The elliptic curves in class 111090.p do not have complex multiplication.Modular form 111090.2.a.p
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.
