Show commands:
SageMath
E = EllipticCurve("ga1")
E.isogeny_class()
Elliptic curves in class 92400ga
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.fb4 | 92400ga1 | \([0, 1, 0, -38808, -10773612]\) | \(-100999381393/723148272\) | \(-46281489408000000\) | \([2]\) | \(589824\) | \(1.8809\) | \(\Gamma_0(N)\)-optimal |
| 92400.fb3 | 92400ga2 | \([0, 1, 0, -1006808, -388293612]\) | \(1763535241378513/4612311396\) | \(295187929344000000\) | \([2, 2]\) | \(1179648\) | \(2.2275\) | |
| 92400.fb2 | 92400ga3 | \([0, 1, 0, -1402808, -54861612]\) | \(4770223741048753/2740574865798\) | \(175396791411072000000\) | \([2]\) | \(2359296\) | \(2.5741\) | |
| 92400.fb1 | 92400ga4 | \([0, 1, 0, -16098808, -24867517612]\) | \(7209828390823479793/49509306\) | \(3168595584000000\) | \([2]\) | \(2359296\) | \(2.5741\) |
Rank
sage: E.rank()
The elliptic curves in class 92400ga have rank \(1\).
Complex multiplication
The elliptic curves in class 92400ga do not have complex multiplication.Modular form 92400.2.a.ga
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
