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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 20808k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20808.ba3 | 20808k1 | \([0, 0, 0, -136119, -19288438]\) | \(61918288/153\) | \(689211400589568\) | \([2]\) | \(147456\) | \(1.7251\) | \(\Gamma_0(N)\)-optimal |
| 20808.ba2 | 20808k2 | \([0, 0, 0, -188139, -3193450]\) | \(40873252/23409\) | \(421797377160815616\) | \([2, 2]\) | \(294912\) | \(2.0716\) | |
| 20808.ba1 | 20808k3 | \([0, 0, 0, -1956819, 1049171150]\) | \(22994537186/111537\) | \(4019480888238360576\) | \([2]\) | \(589824\) | \(2.4182\) | |
| 20808.ba4 | 20808k4 | \([0, 0, 0, 748221, -25478818]\) | \(1285471294/751689\) | \(-27088764888772380672\) | \([2]\) | \(589824\) | \(2.4182\) |
Rank
sage: E.rank()
The elliptic curves in class 20808k have rank \(0\).
Complex multiplication
The elliptic curves in class 20808k do not have complex multiplication.Modular form 20808.2.a.k
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 Cremona 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 Cremona labels.
