Show commands:
SageMath
E = EllipticCurve("hr1")
E.isogeny_class()
Elliptic curves in class 394944.hr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 394944.hr1 | 394944hr1 | \([0, 1, 0, -1533473, 730368351]\) | \(858729462625/38148\) | \(17716087102636032\) | \([2]\) | \(5898240\) | \(2.1951\) | \(\Gamma_0(N)\)-optimal |
| 394944.hr2 | 394944hr2 | \([0, 1, 0, -1456033, 807514079]\) | \(-735091890625/181908738\) | \(-84479161348919918592\) | \([2]\) | \(11796480\) | \(2.5417\) |
Rank
sage: E.rank()
The elliptic curves in class 394944.hr have rank \(1\).
Complex multiplication
The elliptic curves in class 394944.hr do not have complex multiplication.Modular form 394944.2.a.hr
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.
