Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 25050.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25050.h1 | 25050h1 | \([1, 0, 1, -46, -112]\) | \(83453453/8016\) | \(1002000\) | \([2]\) | \(5760\) | \(-0.11095\) | \(\Gamma_0(N)\)-optimal |
25050.h2 | 25050h2 | \([1, 0, 1, 54, -512]\) | \(143055667/1004004\) | \(-125500500\) | \([2]\) | \(11520\) | \(0.23562\) |
Rank
sage: E.rank()
The elliptic curves in class 25050.h have rank \(1\).
Complex multiplication
The elliptic curves in class 25050.h do not have complex multiplication.Modular form 25050.2.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.