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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 6930.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.bi1 | 6930bm3 | \([1, -1, 1, -7772, 263621]\) | \(71210194441849/631496250\) | \(460360766250\) | \([2]\) | \(16384\) | \(1.0612\) | |
| 6930.bi2 | 6930bm2 | \([1, -1, 1, -842, -2491]\) | \(90458382169/48024900\) | \(35010152100\) | \([2, 2]\) | \(8192\) | \(0.71467\) | |
| 6930.bi3 | 6930bm1 | \([1, -1, 1, -662, -6379]\) | \(43949604889/55440\) | \(40415760\) | \([2]\) | \(4096\) | \(0.36810\) | \(\Gamma_0(N)\)-optimal |
| 6930.bi4 | 6930bm4 | \([1, -1, 1, 3208, -21931]\) | \(5009866738631/3163773690\) | \(-2306391020010\) | \([2]\) | \(16384\) | \(1.0612\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.bi do not have complex multiplication.Modular form 6930.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
