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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 281775.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 281775.ba1 | 281775ba2 | \([0, -1, 1, -31033783, -55287614157]\) | \(30326094659584/5430160125\) | \(591866873402972501953125\) | \([]\) | \(38071296\) | \(3.2807\) | |
| 281775.ba2 | 281775ba1 | \([0, -1, 1, -8925283, 10258561218]\) | \(721403674624/616005\) | \(67142210350675078125\) | \([]\) | \(12690432\) | \(2.7314\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 281775.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 281775.ba do not have complex multiplication.Modular form 281775.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
