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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 229320.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.j1 | 229320bg3 | \([0, 0, 0, -2565003, 1580679142]\) | \(10625310339698/3855735\) | \(677256057966458880\) | \([2]\) | \(4718592\) | \(2.3899\) | |
| 229320.j2 | 229320bg4 | \([0, 0, 0, -1330203, -578492138]\) | \(1481943889298/34543665\) | \(6067560759651256320\) | \([2]\) | \(4718592\) | \(2.3899\) | |
| 229320.j3 | 229320bg2 | \([0, 0, 0, -183603, 17051902]\) | \(7793764996/3080025\) | \(270501679957017600\) | \([2, 2]\) | \(2359296\) | \(2.0433\) | |
| 229320.j4 | 229320bg1 | \([0, 0, 0, 36897, 1925602]\) | \(253012016/219375\) | \(-4816625355360000\) | \([2]\) | \(1179648\) | \(1.6968\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229320.j have rank \(0\).
Complex multiplication
The elliptic curves in class 229320.j do not have complex multiplication.Modular form 229320.2.a.j
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.
