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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 388080.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.bl1 | 388080bl3 | \([0, 0, 0, -12932984883, 566066560498418]\) | \(680995599504466943307169/52207031250000000\) | \(18340227314640000000000000000\) | \([2]\) | \(495452160\) | \(4.4715\) | |
| 388080.bl2 | 388080bl2 | \([0, 0, 0, -862144563, 7599476421362]\) | \(201738262891771037089/45727545600000000\) | \(16063996759910881689600000000\) | \([2, 2]\) | \(247726080\) | \(4.1249\) | |
| 388080.bl3 | 388080bl1 | \([0, 0, 0, -284117043, -1741563907342]\) | \(7220044159551112609/448454983680000\) | \(157541353035169404026880000\) | \([2]\) | \(123863040\) | \(3.7783\) | \(\Gamma_0(N)\)-optimal |
| 388080.bl4 | 388080bl4 | \([0, 0, 0, 1960255437, 46958973381362]\) | \(2371297246710590562911/4084000833203280000\) | \(-1434701453822416199994900480000\) | \([2]\) | \(495452160\) | \(4.4715\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.bl do not have complex multiplication.Modular form 388080.2.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.
