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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 185150.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185150.s1 | 185150ca4 | \([1, -1, 0, -484004417, -4098350961759]\) | \(5421065386069310769/1919709260\) | \(4440404170713002187500\) | \([2]\) | \(38928384\) | \(3.5082\) | |
| 185150.s2 | 185150ca2 | \([1, -1, 0, -30386917, -63423299259]\) | \(1341518286067569/24894528400\) | \(57582556920777306250000\) | \([2, 2]\) | \(19464192\) | \(3.1616\) | |
| 185150.s3 | 185150ca1 | \([1, -1, 0, -3936917, 1511450741]\) | \(2917464019569/1262240000\) | \(2919637820802500000000\) | \([2]\) | \(9732096\) | \(2.8150\) | \(\Gamma_0(N)\)-optimal |
| 185150.s4 | 185150ca3 | \([1, -1, 0, 30583, -184637036759]\) | \(1367631/6366992112460\) | \(-14727239650375063702187500\) | \([2]\) | \(38928384\) | \(3.5082\) |
Rank
sage: E.rank()
The elliptic curves in class 185150.s have rank \(1\).
Complex multiplication
The elliptic curves in class 185150.s do not have complex multiplication.Modular form 185150.2.a.s
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.
