Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 10164.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10164.w1 | 10164s2 | \([0, 1, 0, -6574, 361073]\) | \(-1108671232/1369599\) | \(-38821250784624\) | \([]\) | \(25920\) | \(1.3010\) | |
10164.w2 | 10164s1 | \([0, 1, 0, 686, -9187]\) | \(1257728/2079\) | \(-58929205104\) | \([]\) | \(8640\) | \(0.75170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10164.w have rank \(0\).
Complex multiplication
The elliptic curves in class 10164.w do not have complex multiplication.Modular form 10164.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.