Show commands:
SageMath
E = EllipticCurve("hj1")
E.isogeny_class()
Elliptic curves in class 33600hj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.gq1 | 33600hj1 | \([0, 1, 0, -128833, -2185537]\) | \(461889917/263424\) | \(134873088000000000\) | \([2]\) | \(368640\) | \(1.9767\) | \(\Gamma_0(N)\)-optimal |
33600.gq2 | 33600hj2 | \([0, 1, 0, 511167, -16905537]\) | \(28849701763/16941456\) | \(-8674025472000000000\) | \([2]\) | \(737280\) | \(2.3233\) |
Rank
sage: E.rank()
The elliptic curves in class 33600hj have rank \(1\).
Complex multiplication
The elliptic curves in class 33600hj do not have complex multiplication.Modular form 33600.2.a.hj
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 Cremona 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 Cremona labels.