Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2736.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2736.h1 | 2736s2 | \([0, 0, 0, -632208, -193481296]\) | \(-9358714467168256/22284891\) | \(-66542327967744\) | \([]\) | \(19200\) | \(1.8939\) | |
2736.h2 | 2736s1 | \([0, 0, 0, 2832, -66256]\) | \(841232384/1121931\) | \(-3350068015104\) | \([]\) | \(3840\) | \(1.0891\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2736.h have rank \(0\).
Complex multiplication
The elliptic curves in class 2736.h do not have complex multiplication.Modular form 2736.2.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.