Show commands:
SageMath
E = EllipticCurve("jy1")
E.isogeny_class()
Elliptic curves in class 388080jy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.jy5 | 388080jy1 | \([0, 0, 0, 1016358, -1298852849]\) | \(84611246065664/580054565475\) | \(-795984480786100359600\) | \([2]\) | \(12582912\) | \(2.6922\) | \(\Gamma_0(N)\)-optimal |
| 388080.jy4 | 388080jy2 | \([0, 0, 0, -13450647, -17319614186]\) | \(12257375872392016/1191317675625\) | \(26156722154775680160000\) | \([2, 2]\) | \(25165824\) | \(3.0388\) | |
| 388080.jy3 | 388080jy3 | \([0, 0, 0, -48457227, 110643438346]\) | \(143279368983686884/22699269140625\) | \(1993552142055843600000000\) | \([2, 2]\) | \(50331648\) | \(3.3853\) | |
| 388080.jy2 | 388080jy4 | \([0, 0, 0, -209916147, -1170611392286]\) | \(11647843478225136004/128410942275\) | \(11277627814790825241600\) | \([2]\) | \(50331648\) | \(3.3853\) | |
| 388080.jy1 | 388080jy5 | \([0, 0, 0, -743032227, 7795560153346]\) | \(258286045443018193442/8440380939375\) | \(1482544605045821264640000\) | \([2]\) | \(100663296\) | \(3.7319\) | |
| 388080.jy6 | 388080jy6 | \([0, 0, 0, 86012493, 615362085394]\) | \(400647648358480318/1163177490234375\) | \(-204310981369687500000000000\) | \([2]\) | \(100663296\) | \(3.7319\) |
Rank
sage: E.rank()
The elliptic curves in class 388080jy have rank \(2\).
Complex multiplication
The elliptic curves in class 388080jy do not have complex multiplication.Modular form 388080.2.a.jy
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
