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SageMath
E = EllipticCurve("gy1")
E.isogeny_class()
Elliptic curves in class 158400gy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.j2 | 158400gy1 | \([0, 0, 0, -17174700, -27395614000]\) | \(5066026756449723/11000000\) | \(1216512000000000000\) | \([2]\) | \(7962624\) | \(2.7170\) | \(\Gamma_0(N)\)-optimal |
| 158400.j3 | 158400gy2 | \([0, 0, 0, -16982700, -28038046000]\) | \(-4898016158612283/236328125000\) | \(-26136000000000000000000\) | \([2]\) | \(15925248\) | \(3.0636\) | |
| 158400.j1 | 158400gy3 | \([0, 0, 0, -22574700, -8744814000]\) | \(15781142246787/8722841600\) | \(703249167207628800000000\) | \([2]\) | \(23887872\) | \(3.2663\) | |
| 158400.j4 | 158400gy4 | \([0, 0, 0, 88017300, -69128046000]\) | \(935355271080573/566899520000\) | \(-45704328200847360000000000\) | \([2]\) | \(47775744\) | \(3.6129\) |
Rank
sage: E.rank()
The elliptic curves in class 158400gy have rank \(0\).
Complex multiplication
The elliptic curves in class 158400gy do not have complex multiplication.Modular form 158400.2.a.gy
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
