Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3648.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3648.h1 | 3648f2 | \([0, -1, 0, -17561, -889893]\) | \(-9358714467168256/22284891\) | \(-1426233024\) | \([]\) | \(4800\) | \(0.99798\) | |
| 3648.h2 | 3648f1 | \([0, -1, 0, 79, -333]\) | \(841232384/1121931\) | \(-71803584\) | \([]\) | \(960\) | \(0.19326\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3648.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3648.h do not have complex multiplication.Modular form 3648.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
