Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 179520.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.h1 | 179520hp3 | \([0, -1, 0, -8161, 157921]\) | \(917333238244/372086055\) | \(24385031700480\) | \([2]\) | \(491520\) | \(1.2665\) | |
| 179520.h2 | 179520hp2 | \([0, -1, 0, -3761, -85839]\) | \(359194138576/7868025\) | \(128909721600\) | \([2, 2]\) | \(245760\) | \(0.91997\) | |
| 179520.h3 | 179520hp1 | \([0, -1, 0, -3741, -86835]\) | \(5655916189696/2805\) | \(2872320\) | \([2]\) | \(122880\) | \(0.57339\) | \(\Gamma_0(N)\)-optimal |
| 179520.h4 | 179520hp4 | \([0, -1, 0, 319, -266175]\) | \(54607676/466681875\) | \(-30584463360000\) | \([2]\) | \(491520\) | \(1.2665\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.h have rank \(1\).
Complex multiplication
The elliptic curves in class 179520.h do not have complex multiplication.Modular form 179520.2.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.
