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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 9744.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9744.g1 | 9744k3 | \([0, -1, 0, -470832, -124181568]\) | \(2818140246756887473/314406208368\) | \(1287807829475328\) | \([2]\) | \(110592\) | \(1.9279\) | |
| 9744.g2 | 9744k2 | \([0, -1, 0, -31792, -1601600]\) | \(867622835347633/227964231936\) | \(933741494009856\) | \([2, 2]\) | \(55296\) | \(1.5813\) | |
| 9744.g3 | 9744k1 | \([0, -1, 0, -11312, 446400]\) | \(39085920587953/1955659776\) | \(8010382442496\) | \([2]\) | \(27648\) | \(1.2347\) | \(\Gamma_0(N)\)-optimal |
| 9744.g4 | 9744k4 | \([0, -1, 0, 79568, -10421312]\) | \(13601087408654927/19267071783792\) | \(-78917926026412032\) | \([4]\) | \(110592\) | \(1.9279\) |
Rank
sage: E.rank()
The elliptic curves in class 9744.g have rank \(0\).
Complex multiplication
The elliptic curves in class 9744.g do not have complex multiplication.Modular form 9744.2.a.g
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.
