Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 30400.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30400.ba1 | 30400ba4 | \([0, 0, 0, -202700, -35126000]\) | \(899466517764/95\) | \(97280000000\) | \([2]\) | \(98304\) | \(1.5366\) | |
| 30400.ba2 | 30400ba3 | \([0, 0, 0, -22700, 434000]\) | \(1263284964/651605\) | \(667243520000000\) | \([2]\) | \(98304\) | \(1.5366\) | |
| 30400.ba3 | 30400ba2 | \([0, 0, 0, -12700, -546000]\) | \(884901456/9025\) | \(2310400000000\) | \([2, 2]\) | \(49152\) | \(1.1900\) | |
| 30400.ba4 | 30400ba1 | \([0, 0, 0, -200, -21000]\) | \(-55296/11875\) | \(-190000000000\) | \([2]\) | \(24576\) | \(0.84346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30400.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 30400.ba do not have complex multiplication.Modular form 30400.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
