Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 570.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
570.h1 | 570h2 | \([1, 1, 1, -30, -75]\) | \(2992209121/54150\) | \(54150\) | \([2]\) | \(96\) | \(-0.29643\) | |
570.h2 | 570h1 | \([1, 1, 1, 0, -3]\) | \(-1/3420\) | \(-3420\) | \([2]\) | \(48\) | \(-0.64300\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 570.h have rank \(0\).
Complex multiplication
The elliptic curves in class 570.h do not have complex multiplication.Modular form 570.2.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.