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SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 202800gi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.eo2 | 202800gi1 | \([0, -1, 0, -3550408, 2711203312]\) | \(-16022066761/998400\) | \(-308421510758400000000\) | \([2]\) | \(7741440\) | \(2.6856\) | \(\Gamma_0(N)\)-optimal |
| 202800.eo1 | 202800gi2 | \([0, -1, 0, -57630408, 168412323312]\) | \(68523370149961/243360\) | \(75177743247360000000\) | \([2]\) | \(15482880\) | \(3.0322\) |
Rank
sage: E.rank()
The elliptic curves in class 202800gi have rank \(0\).
Complex multiplication
The elliptic curves in class 202800gi do not have complex multiplication.Modular form 202800.2.a.gi
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
