Show commands:
SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 188760.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.cy1 | 188760n2 | \([0, 1, 0, -825040, 203609888]\) | \(22784591413352662/6597644551875\) | \(17984440112221440000\) | \([2]\) | \(6580224\) | \(2.4009\) | |
| 188760.cy2 | 188760n1 | \([0, 1, 0, 137240, 21161600]\) | \(209741642018356/262704572325\) | \(-358051620622924800\) | \([2]\) | \(3290112\) | \(2.0543\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 188760.cy do not have complex multiplication.Modular form 188760.2.a.cy
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.
