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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 57222.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.bt1 | 57222bi2 | \([1, -1, 1, -7762739, 8305431923]\) | \(2940001530995593/8673562656\) | \(152622504754981959456\) | \([2]\) | \(2211840\) | \(2.7429\) | |
| 57222.bt2 | 57222bi1 | \([1, -1, 1, -688019, 11030195]\) | \(2046931732873/1181672448\) | \(20793048481520206848\) | \([2]\) | \(1105920\) | \(2.3963\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57222.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 57222.bt do not have complex multiplication.Modular form 57222.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
