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SageMath
E = EllipticCurve("gy1")
E.isogeny_class()
Elliptic curves in class 388080.gy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.gy1 | 388080gy3 | \([0, 0, 0, -11061603, 2999471202]\) | \(15781142246787/8722841600\) | \(82736561272810320691200\) | \([2]\) | \(35831808\) | \(3.0880\) | |
| 388080.gy2 | 388080gy1 | \([0, 0, 0, -8415603, 9396695602]\) | \(5066026756449723/11000000\) | \(143121420288000000\) | \([2]\) | \(11943936\) | \(2.5387\) | \(\Gamma_0(N)\)-optimal |
| 388080.gy3 | 388080gy2 | \([0, 0, 0, -8321523, 9617049778]\) | \(-4898016158612283/236328125000\) | \(-3074874264000000000000\) | \([2]\) | \(23887872\) | \(2.8853\) | |
| 388080.gy4 | 388080gy4 | \([0, 0, 0, 43128477, 23710919778]\) | \(935355271080573/566899520000\) | \(-5377068508501491056640000\) | \([2]\) | \(71663616\) | \(3.4346\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.gy have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.gy do not have complex multiplication.Modular form 388080.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
