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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 116025.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116025.bq1 | 116025bg6 | \([1, 0, 1, -1014476, -393091027]\) | \(7389727131216686257/6115533215337\) | \(95555206489640625\) | \([2]\) | \(1572864\) | \(2.1866\) | |
| 116025.bq2 | 116025bg4 | \([1, 0, 1, -77351, -3247027]\) | \(3275619238041697/1605271262049\) | \(25082363469515625\) | \([2, 2]\) | \(786432\) | \(1.8400\) | |
| 116025.bq3 | 116025bg2 | \([1, 0, 1, -41226, 3183223]\) | \(495909170514577/6224736609\) | \(97261509515625\) | \([2, 2]\) | \(393216\) | \(1.4935\) | |
| 116025.bq4 | 116025bg1 | \([1, 0, 1, -41101, 3203723]\) | \(491411892194497/78897\) | \(1232765625\) | \([2]\) | \(196608\) | \(1.1469\) | \(\Gamma_0(N)\)-optimal |
| 116025.bq5 | 116025bg3 | \([1, 0, 1, -7101, 8301973]\) | \(-2533811507137/1904381781393\) | \(-29755965334265625\) | \([2]\) | \(786432\) | \(1.8400\) | |
| 116025.bq6 | 116025bg5 | \([1, 0, 1, 281774, -24794527]\) | \(158346567380527343/108665074944153\) | \(-1697891796002390625\) | \([2]\) | \(1572864\) | \(2.1866\) |
Rank
sage: E.rank()
The elliptic curves in class 116025.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 116025.bq do not have complex multiplication.Modular form 116025.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
