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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 101430.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.bq1 | 101430cn6 | \([1, -1, 0, -37348299, -87843106625]\) | \(67176973097223766561/91487391870\) | \(7846518721096836270\) | \([2]\) | \(6291456\) | \(2.8997\) | |
| 101430.bq2 | 101430cn4 | \([1, -1, 0, -2354949, -1346544095]\) | \(16840406336564161/604708416900\) | \(51863495253563844900\) | \([2, 2]\) | \(3145728\) | \(2.5531\) | |
| 101430.bq3 | 101430cn2 | \([1, -1, 0, -370449, 58085005]\) | \(65553197996161/20996010000\) | \(1800746334177210000\) | \([2, 2]\) | \(1572864\) | \(2.2065\) | |
| 101430.bq4 | 101430cn1 | \([1, -1, 0, -335169, 74758333]\) | \(48551226272641/9273600\) | \(795360699705600\) | \([2]\) | \(786432\) | \(1.8600\) | \(\Gamma_0(N)\)-optimal |
| 101430.bq5 | 101430cn5 | \([1, -1, 0, 886401, -4770057965]\) | \(898045580910239/115117148363070\) | \(-9873151275682013551470\) | \([2]\) | \(6291456\) | \(2.8997\) | |
| 101430.bq6 | 101430cn3 | \([1, -1, 0, 1049571, 395197753]\) | \(1490881681033919/1650501562500\) | \(-141557116720064062500\) | \([2]\) | \(3145728\) | \(2.5531\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 101430.bq do not have complex multiplication.Modular form 101430.2.a.bq
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
