Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 18810.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18810.s1 | 18810y3 | \([1, -1, 1, -82103, -9034383]\) | \(83959202297868841/25036110\) | \(18251324190\) | \([2]\) | \(49152\) | \(1.3338\) | |
| 18810.s2 | 18810y2 | \([1, -1, 1, -5153, -138963]\) | \(20753798525641/353816100\) | \(257931936900\) | \([2, 2]\) | \(24576\) | \(0.98722\) | |
| 18810.s3 | 18810y1 | \([1, -1, 1, -653, 3237]\) | \(42180533641/18810000\) | \(13712490000\) | \([2]\) | \(12288\) | \(0.64064\) | \(\Gamma_0(N)\)-optimal |
| 18810.s4 | 18810y4 | \([1, -1, 1, -203, -398343]\) | \(-1263214441/94053968910\) | \(-68565343335390\) | \([2]\) | \(49152\) | \(1.3338\) |
Rank
sage: E.rank()
The elliptic curves in class 18810.s have rank \(1\).
Complex multiplication
The elliptic curves in class 18810.s do not have complex multiplication.Modular form 18810.2.a.s
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.
