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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 285912.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 285912.bi1 | 285912bi3 | \([0, 0, 0, -2288379, 1332415622]\) | \(37736227588/33\) | \(1158945545438208\) | \([2]\) | \(4644864\) | \(2.1908\) | |
| 285912.bi2 | 285912bi4 | \([0, 0, 0, -338979, -46901842]\) | \(122657188/43923\) | \(1542556520978254848\) | \([2]\) | \(4644864\) | \(2.1908\) | |
| 285912.bi3 | 285912bi2 | \([0, 0, 0, -144039, 20508410]\) | \(37642192/1089\) | \(9561300749865216\) | \([2, 2]\) | \(2322432\) | \(1.8443\) | |
| 285912.bi4 | 285912bi1 | \([0, 0, 0, 2166, 1063145]\) | \(2048/891\) | \(-488930151981744\) | \([2]\) | \(1161216\) | \(1.4977\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 285912.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 285912.bi do not have complex multiplication.Modular form 285912.2.a.bi
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.
