Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 20097.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20097.l1 | 20097h3 | \([1, -1, 0, -480201, -127946386]\) | \(16798320881842096017/2132227789307\) | \(1554394058404803\) | \([2]\) | \(172032\) | \(1.9368\) | |
| 20097.l2 | 20097h4 | \([1, -1, 0, -190491, 30741092]\) | \(1048626554636928177/48569076788309\) | \(35406856978677261\) | \([2]\) | \(172032\) | \(1.9368\) | |
| 20097.l3 | 20097h2 | \([1, -1, 0, -32586, -1629433]\) | \(5249244962308257/1448621666569\) | \(1056045194928801\) | \([2, 2]\) | \(86016\) | \(1.5903\) | |
| 20097.l4 | 20097h1 | \([1, -1, 0, 5259, -168616]\) | \(22062729659823/29354283343\) | \(-21399272557047\) | \([2]\) | \(43008\) | \(1.2437\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20097.l have rank \(1\).
Complex multiplication
The elliptic curves in class 20097.l do not have complex multiplication.Modular form 20097.2.a.l
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.
