Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 39600.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.h1 | 39600do4 | \([0, 0, 0, -1267275, -549103750]\) | \(4824238966273/66\) | \(3079296000000\) | \([2]\) | \(393216\) | \(1.9522\) | |
| 39600.h2 | 39600do2 | \([0, 0, 0, -79275, -8563750]\) | \(1180932193/4356\) | \(203233536000000\) | \([2, 2]\) | \(196608\) | \(1.6056\) | |
| 39600.h3 | 39600do3 | \([0, 0, 0, -43275, -16375750]\) | \(-192100033/2371842\) | \(-110660660352000000\) | \([2]\) | \(393216\) | \(1.9522\) | |
| 39600.h4 | 39600do1 | \([0, 0, 0, -7275, 4250]\) | \(912673/528\) | \(24634368000000\) | \([2]\) | \(98304\) | \(1.2591\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.h have rank \(1\).
Complex multiplication
The elliptic curves in class 39600.h do not have complex multiplication.Modular form 39600.2.a.h
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.
