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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 380880.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 380880.e1 | 380880e4 | \([0, 0, 0, -299385963, -1776943945062]\) | \(248656466619387/29607177800\) | \(353358276768117537376665600\) | \([2]\) | \(131383296\) | \(3.8252\) | |
| 380880.e2 | 380880e3 | \([0, 0, 0, -290244843, -1903217548518]\) | \(226568219476347/3893440\) | \(46467760567846474874880\) | \([2]\) | \(65691648\) | \(3.4786\) | |
| 380880.e3 | 380880e2 | \([0, 0, 0, -70857963, 229228883738]\) | \(2403250125069123/4232000000\) | \(69284547873570816000000\) | \([2]\) | \(43794432\) | \(3.2759\) | |
| 380880.e4 | 380880e1 | \([0, 0, 0, -5854443, 1079529242]\) | \(1355469437763/753664000\) | \(12338674264788959232000\) | \([2]\) | \(21897216\) | \(2.9293\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 380880.e have rank \(1\).
Complex multiplication
The elliptic curves in class 380880.e do not have complex multiplication.Modular form 380880.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
