Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 19845.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19845.h1 | 19845g2 | \([0, 0, 1, -5292, 141230]\) | \(2359296/125\) | \(868381975125\) | \([]\) | \(25920\) | \(1.0476\) | |
| 19845.h2 | 19845g1 | \([0, 0, 1, -882, -10033]\) | \(884736/5\) | \(428830605\) | \([]\) | \(8640\) | \(0.49832\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19845.h have rank \(1\).
Complex multiplication
The elliptic curves in class 19845.h do not have complex multiplication.Modular form 19845.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
