Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 7440.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7440.j1 | 7440o5 | \([0, -1, 0, -4920320, 4202499840]\) | \(3216206300355197383681/57660\) | \(236175360\) | \([4]\) | \(98304\) | \(2.0750\) | |
| 7440.j2 | 7440o4 | \([0, -1, 0, -307520, 65740800]\) | \(785209010066844481/3324675600\) | \(13617871257600\) | \([2, 4]\) | \(49152\) | \(1.7284\) | |
| 7440.j3 | 7440o6 | \([0, -1, 0, -302720, 67887360]\) | \(-749011598724977281/51173462246460\) | \(-209606501361500160\) | \([4]\) | \(98304\) | \(2.0750\) | |
| 7440.j4 | 7440o3 | \([0, -1, 0, -59200, -4302848]\) | \(5601911201812801/1271193750000\) | \(5206809600000000\) | \([2]\) | \(49152\) | \(1.7284\) | |
| 7440.j5 | 7440o2 | \([0, -1, 0, -19520, 998400]\) | \(200828550012481/12454560000\) | \(51013877760000\) | \([2, 2]\) | \(24576\) | \(1.3818\) | |
| 7440.j6 | 7440o1 | \([0, -1, 0, 960, 64512]\) | \(23862997439/457113600\) | \(-1872337305600\) | \([2]\) | \(12288\) | \(1.0353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7440.j have rank \(0\).
Complex multiplication
The elliptic curves in class 7440.j do not have complex multiplication.Modular form 7440.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
