Show commands:
SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 101400cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101400.bc5 | 101400cb1 | \([0, -1, 0, -64783, 6358312]\) | \(24918016/45\) | \(54301601250000\) | \([2]\) | \(368640\) | \(1.5275\) | \(\Gamma_0(N)\)-optimal |
| 101400.bc4 | 101400cb2 | \([0, -1, 0, -85908, 1879812]\) | \(3631696/2025\) | \(39097152900000000\) | \([2, 2]\) | \(737280\) | \(1.8740\) | |
| 101400.bc6 | 101400cb3 | \([0, -1, 0, 336592, 14554812]\) | \(54607676/32805\) | \(-2533495507920000000\) | \([2]\) | \(1474560\) | \(2.2206\) | |
| 101400.bc2 | 101400cb4 | \([0, -1, 0, -846408, -297757188]\) | \(868327204/5625\) | \(434412810000000000\) | \([2, 2]\) | \(1474560\) | \(2.2206\) | |
| 101400.bc3 | 101400cb5 | \([0, -1, 0, -339408, -651643188]\) | \(-27995042/1171875\) | \(-181005337500000000000\) | \([2]\) | \(2949120\) | \(2.5672\) | |
| 101400.bc1 | 101400cb6 | \([0, -1, 0, -13521408, -19132807188]\) | \(1770025017602/75\) | \(11584341600000000\) | \([2]\) | \(2949120\) | \(2.5672\) |
Rank
sage: E.rank()
The elliptic curves in class 101400cb have rank \(0\).
Complex multiplication
The elliptic curves in class 101400cb do not have complex multiplication.Modular form 101400.2.a.cb
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
