Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 224448.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224448.bh1 | 224448bo3 | \([0, -1, 0, -13971777, 20105545185]\) | \(1150638118585800835537/31752757008504\) | \(8323794733237272576\) | \([2]\) | \(12386304\) | \(2.7336\) | |
| 224448.bh2 | 224448bo4 | \([0, -1, 0, -3900737, -2680157727]\) | \(25039399590518087377/2641281025170312\) | \(692395973062246268928\) | \([2]\) | \(12386304\) | \(2.7336\) | |
| 224448.bh3 | 224448bo2 | \([0, -1, 0, -908097, 287942625]\) | \(315922815546536017/46479778841664\) | \(12184395144669167616\) | \([2, 2]\) | \(6193152\) | \(2.3870\) | |
| 224448.bh4 | 224448bo1 | \([0, -1, 0, 95423, 24418273]\) | \(366554400441263/1197281046528\) | \(-313860042661036032\) | \([2]\) | \(3096576\) | \(2.0405\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224448.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 224448.bh do not have complex multiplication.Modular form 224448.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
