Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 372645bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 372645.bh2 | 372645bh1 | \([1, -1, 1, -4597508, -3644038394]\) | \(2803221/125\) | \(479229759669698753625\) | \([2]\) | \(15482880\) | \(2.7309\) | \(\Gamma_0(N)\)-optimal |
| 372645.bh1 | 372645bh2 | \([1, -1, 1, -12423053, 12060265312]\) | \(55306341/15625\) | \(59903719958712344203125\) | \([2]\) | \(30965760\) | \(3.0775\) |
Rank
sage: E.rank()
The elliptic curves in class 372645bh have rank \(0\).
Complex multiplication
The elliptic curves in class 372645bh do not have complex multiplication.Modular form 372645.2.a.bh
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.
