Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 7744.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7744.h1 | 7744bg2 | \([0, 1, 0, -3329, -77057]\) | \(-128667913/4096\) | \(-129922760704\) | \([]\) | \(9216\) | \(0.90851\) | |
| 7744.h2 | 7744bg1 | \([0, 1, 0, 191, -321]\) | \(24167/16\) | \(-507510784\) | \([]\) | \(3072\) | \(0.35921\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7744.h have rank \(1\).
Complex multiplication
The elliptic curves in class 7744.h do not have complex multiplication.Modular form 7744.2.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.
