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SageMath
E = EllipticCurve("nq1")
E.isogeny_class()
Elliptic curves in class 388080.nq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.nq1 | 388080nq5 | \([0, 0, 0, -93492147, 347928497714]\) | \(257260669489908001/14267882475\) | \(5012279028795922329600\) | \([2]\) | \(50331648\) | \(3.2293\) | |
| 388080.nq2 | 388080nq3 | \([0, 0, 0, -6174147, 4786221314]\) | \(74093292126001/14707625625\) | \(5166759931807541760000\) | \([2, 2]\) | \(25165824\) | \(2.8827\) | |
| 388080.nq3 | 388080nq2 | \([0, 0, 0, -1905267, -945176974]\) | \(2177286259681/161417025\) | \(56705483151810662400\) | \([2, 2]\) | \(12582912\) | \(2.5361\) | |
| 388080.nq4 | 388080nq1 | \([0, 0, 0, -1869987, -984246046]\) | \(2058561081361/12705\) | \(4463241491681280\) | \([2]\) | \(6291456\) | \(2.1896\) | \(\Gamma_0(N)\)-optimal |
| 388080.nq5 | 388080nq4 | \([0, 0, 0, 1799133, -4176154654]\) | \(1833318007919/22507682505\) | \(-7906904560244380078080\) | \([2]\) | \(25165824\) | \(2.8827\) | |
| 388080.nq6 | 388080nq6 | \([0, 0, 0, 12841773, 28453435346]\) | \(666688497209279/1381398046875\) | \(-485282414745374400000000\) | \([2]\) | \(50331648\) | \(3.2293\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.nq have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.nq do not have complex multiplication.Modular form 388080.2.a.nq
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.
