Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 87360.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.j1 | 87360dw4 | \([0, -1, 0, -2620801, 1633922785]\) | \(60754168345375814408/61425\) | \(2012774400\) | \([2]\) | \(786432\) | \(1.9727\) | |
| 87360.j2 | 87360dw2 | \([0, -1, 0, -163801, 25570585]\) | \(118663201655107264/3773030625\) | \(15454333440000\) | \([2, 2]\) | \(393216\) | \(1.6262\) | |
| 87360.j3 | 87360dw3 | \([0, -1, 0, -156801, 27848385]\) | \(-13011370125062408/2656235120175\) | \(-87039512417894400\) | \([2]\) | \(786432\) | \(1.9727\) | |
| 87360.j4 | 87360dw1 | \([0, -1, 0, -10676, 366210]\) | \(2102858800664896/329199609375\) | \(21068775000000\) | \([2]\) | \(196608\) | \(1.2796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87360.j have rank \(2\).
Complex multiplication
The elliptic curves in class 87360.j do not have complex multiplication.Modular form 87360.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
