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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 37440.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.bl1 | 37440bk4 | \([0, 0, 0, -7788, -215152]\) | \(2186875592/428415\) | \(10233922682880\) | \([2]\) | \(49152\) | \(1.2131\) | |
| 37440.bl2 | 37440bk2 | \([0, 0, 0, -2388, 41888]\) | \(504358336/38025\) | \(113542041600\) | \([2, 2]\) | \(24576\) | \(0.86651\) | |
| 37440.bl3 | 37440bk1 | \([0, 0, 0, -2343, 43652]\) | \(30488290624/195\) | \(9097920\) | \([2]\) | \(12288\) | \(0.51993\) | \(\Gamma_0(N)\)-optimal |
| 37440.bl4 | 37440bk3 | \([0, 0, 0, 2292, 186032]\) | \(55742968/658125\) | \(-15721205760000\) | \([2]\) | \(49152\) | \(1.2131\) |
Rank
sage: E.rank()
The elliptic curves in class 37440.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 37440.bl do not have complex multiplication.Modular form 37440.2.a.bl
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.
