Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 158400.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.s1 | 158400ke3 | \([0, 0, 0, -1454700, 641486000]\) | \(228027144098/12890625\) | \(19245600000000000000\) | \([2]\) | \(4718592\) | \(2.4549\) | |
158400.s2 | 158400ke2 | \([0, 0, 0, -266700, -40426000]\) | \(2810381476/680625\) | \(508083840000000000\) | \([2, 2]\) | \(2359296\) | \(2.1084\) | |
158400.s3 | 158400ke1 | \([0, 0, 0, -248700, -47734000]\) | \(9115564624/825\) | \(153964800000000\) | \([2]\) | \(1179648\) | \(1.7618\) | \(\Gamma_0(N)\)-optimal |
158400.s4 | 158400ke4 | \([0, 0, 0, 633300, -254626000]\) | \(18814587262/29648025\) | \(-44264264140800000000\) | \([2]\) | \(4718592\) | \(2.4549\) |
Rank
sage: E.rank()
The elliptic curves in class 158400.s have rank \(0\).
Complex multiplication
The elliptic curves in class 158400.s do not have complex multiplication.Modular form 158400.2.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.