Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 42320.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42320.ba1 | 42320z3 | \([0, -1, 0, -21865, -1236900]\) | \(488095744/125\) | \(296071778000\) | \([2]\) | \(71280\) | \(1.1871\) | |
| 42320.ba2 | 42320z4 | \([0, -1, 0, -19220, -1550068]\) | \(-20720464/15625\) | \(-592143556000000\) | \([2]\) | \(142560\) | \(1.5337\) | |
| 42320.ba3 | 42320z1 | \([0, -1, 0, -705, 5192]\) | \(16384/5\) | \(11842871120\) | \([2]\) | \(23760\) | \(0.63780\) | \(\Gamma_0(N)\)-optimal |
| 42320.ba4 | 42320z2 | \([0, -1, 0, 1940, 32700]\) | \(21296/25\) | \(-947429689600\) | \([2]\) | \(47520\) | \(0.98437\) |
Rank
sage: E.rank()
The elliptic curves in class 42320.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 42320.ba do not have complex multiplication.Modular form 42320.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
