Show commands:
SageMath
E = EllipticCurve("ih1")
E.isogeny_class()
Elliptic curves in class 141120.ih
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.ih1 | 141120ib2 | \([0, 0, 0, -54012, 3056816]\) | \(4253563312/1476225\) | \(6047754364108800\) | \([2]\) | \(983040\) | \(1.7298\) | |
| 141120.ih2 | 141120ib1 | \([0, 0, 0, -22512, -1264984]\) | \(4927700992/151875\) | \(38887309440000\) | \([2]\) | \(491520\) | \(1.3833\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.ih have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.ih do not have complex multiplication.Modular form 141120.2.a.ih
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
