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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 14586.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14586.i1 | 14586k3 | \([1, 1, 1, -2509653144, -48392477978535]\) | \(1748094148784980747354970849498497/887694600425282263291392\) | \(887694600425282263291392\) | \([2]\) | \(9455616\) | \(3.9280\) | |
| 14586.i2 | 14586k4 | \([1, 1, 1, -343304344, 1346305732697]\) | \(4474676144192042711273397261697/1806328356954994499451382272\) | \(1806328356954994499451382272\) | \([2]\) | \(9455616\) | \(3.9280\) | |
| 14586.i3 | 14586k2 | \([1, 1, 1, -157701784, -747588108199]\) | \(433744050935826360922067531137/9612122270219882316693504\) | \(9612122270219882316693504\) | \([2, 2]\) | \(4727808\) | \(3.5814\) | |
| 14586.i4 | 14586k1 | \([1, 1, 1, 895336, -35804233639]\) | \(79374649975090937760383/553856914190911653543936\) | \(-553856914190911653543936\) | \([4]\) | \(2363904\) | \(3.2349\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14586.i have rank \(0\).
Complex multiplication
The elliptic curves in class 14586.i do not have complex multiplication.Modular form 14586.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
