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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 51984.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51984.ci1 | 51984cr4 | \([0, 0, 0, -5277459, -4666383470]\) | \(115714886617/1539\) | \(216196023567200256\) | \([2]\) | \(1105920\) | \(2.4697\) | |
| 51984.ci2 | 51984cr2 | \([0, 0, 0, -338979, -68658590]\) | \(30664297/3249\) | \(456413827530756096\) | \([2, 2]\) | \(552960\) | \(2.1231\) | |
| 51984.ci3 | 51984cr1 | \([0, 0, 0, -79059, 7394002]\) | \(389017/57\) | \(8007260132118528\) | \([2]\) | \(276480\) | \(1.7765\) | \(\Gamma_0(N)\)-optimal |
| 51984.ci4 | 51984cr3 | \([0, 0, 0, 440781, -338299598]\) | \(67419143/390963\) | \(-54921797246200983552\) | \([2]\) | \(1105920\) | \(2.4697\) |
Rank
sage: E.rank()
The elliptic curves in class 51984.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 51984.ci do not have complex multiplication.Modular form 51984.2.a.ci
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.
