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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 15210.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.bq1 | 15210bn5 | \([1, -1, 1, -13711847, 19546461861]\) | \(81025909800741361/11088090\) | \(39016147508906490\) | \([2]\) | \(688128\) | \(2.5959\) | |
| 15210.bq2 | 15210bn3 | \([1, -1, 1, -1285277, -560081271]\) | \(66730743078481/60937500\) | \(214423447935937500\) | \([2]\) | \(344064\) | \(2.2493\) | |
| 15210.bq3 | 15210bn4 | \([1, -1, 1, -859397, 303773721]\) | \(19948814692561/231344100\) | \(814040608519160100\) | \([2, 2]\) | \(344064\) | \(2.2493\) | |
| 15210.bq4 | 15210bn6 | \([1, -1, 1, -174947, 773853981]\) | \(-168288035761/73415764890\) | \(-258331264665730351290\) | \([2]\) | \(688128\) | \(2.5959\) | |
| 15210.bq5 | 15210bn2 | \([1, -1, 1, -98897, -4380879]\) | \(30400540561/15210000\) | \(53520092604810000\) | \([2, 2]\) | \(172032\) | \(1.9027\) | |
| 15210.bq6 | 15210bn1 | \([1, -1, 1, 22783, -535791]\) | \(371694959/249600\) | \(-878278442745600\) | \([4]\) | \(86016\) | \(1.5561\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15210.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.bq do not have complex multiplication.Modular form 15210.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
