Show commands:
SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 115920.fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.fh1 | 115920ey2 | \([0, 0, 0, -141627, -20514454]\) | \(105214211150329/2028600\) | \(6057367142400\) | \([2]\) | \(442368\) | \(1.5755\) | |
| 115920.fh2 | 115920ey1 | \([0, 0, 0, -9147, -298006]\) | \(28344726649/3554880\) | \(10614814801920\) | \([2]\) | \(221184\) | \(1.2289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.fh have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.fh do not have complex multiplication.Modular form 115920.2.a.fh
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.
