Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 6384.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6384.h1 | 6384w2 | \([0, -1, 0, -4964, 136284]\) | \(52852623679312/8379\) | \(2145024\) | \([2]\) | \(3072\) | \(0.61817\) | |
| 6384.h2 | 6384w1 | \([0, -1, 0, -309, 2220]\) | \(-204589760512/2600283\) | \(-41604528\) | \([2]\) | \(1536\) | \(0.27160\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6384.h have rank \(1\).
Complex multiplication
The elliptic curves in class 6384.h do not have complex multiplication.Modular form 6384.2.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.
