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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 116610.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116610.p1 | 116610j4 | \([1, 1, 0, -152215937, 584890957461]\) | \(80806068814333255301089/16138368492187500000\) | \(77896822283407054687500000\) | \([2]\) | \(54190080\) | \(3.6843\) | |
| 116610.p2 | 116610j2 | \([1, 1, 0, -47111457, -116303070411]\) | \(2395759505028485296609/176228681616000000\) | \(850622186482243344000000\) | \([2, 2]\) | \(27095040\) | \(3.3377\) | |
| 116610.p3 | 116610j1 | \([1, 1, 0, -46246177, -121067821259]\) | \(2266162893640266805729/13755875328000\) | \(66396982836068352000\) | \([2]\) | \(13547520\) | \(2.9911\) | \(\Gamma_0(N)\)-optimal |
| 116610.p4 | 116610j3 | \([1, 1, 0, 44148543, -512535738411]\) | \(1971572306805346063391/24653689275098988000\) | \(-118998649276251271169292000\) | \([2]\) | \(54190080\) | \(3.6843\) |
Rank
sage: E.rank()
The elliptic curves in class 116610.p have rank \(0\).
Complex multiplication
The elliptic curves in class 116610.p do not have complex multiplication.Modular form 116610.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
