Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 64400.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.h1 | 64400ci2 | \([0, 1, 0, -148, 408]\) | \(11279504/3703\) | \(118496000\) | \([2]\) | \(23040\) | \(0.25222\) | |
| 64400.h2 | 64400ci1 | \([0, 1, 0, 27, 58]\) | \(1048576/1127\) | \(-2254000\) | \([2]\) | \(11520\) | \(-0.094350\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.h have rank \(0\).
Complex multiplication
The elliptic curves in class 64400.h do not have complex multiplication.Modular form 64400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
