Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 303600h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303600.h2 | 303600h1 | \([0, -1, 0, -472208, -122177088]\) | \(1455575263037/34197504\) | \(273580032000000000\) | \([2]\) | \(3870720\) | \(2.1314\) | \(\Gamma_0(N)\)-optimal |
303600.h1 | 303600h2 | \([0, -1, 0, -7512208, -7922497088]\) | \(5860525983613757/3351744\) | \(26813952000000000\) | \([2]\) | \(7741440\) | \(2.4779\) |
Rank
sage: E.rank()
The elliptic curves in class 303600h have rank \(1\).
Complex multiplication
The elliptic curves in class 303600h do not have complex multiplication.Modular form 303600.2.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 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.