Show commands for:
SageMath
sage: E = EllipticCurve("ie1")
sage: E.isogeny_class()
Elliptic curves in class 177870.ie
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
177870.ie1 | 177870j3 | [1, 0, 0, -2214605, 1268320395] | [2] | 3932160 | |
177870.ie2 | 177870j2 | [1, 0, 0, -139455, 19495125] | [2, 2] | 1966080 | |
177870.ie3 | 177870j1 | [1, 0, 0, -20875, -734623] | [2] | 983040 | \(\Gamma_0(N)\)-optimal |
177870.ie4 | 177870j4 | [1, 0, 0, 38415, 65848047] | [2] | 3932160 |
Rank
sage: E.rank()
The elliptic curves in class 177870.ie have rank \(0\).
Complex multiplication
The elliptic curves in class 177870.ie do not have complex multiplication.Modular form 177870.2.a.ie
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.