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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 20280.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20280.s1 | 20280y3 | \([0, 1, 0, -94910456, -355924440000]\) | \(19129597231400697604/26325\) | \(130115324851200\) | \([2]\) | \(1032192\) | \(2.8746\) | |
| 20280.s2 | 20280y2 | \([0, 1, 0, -5931956, -5562698400]\) | \(18681746265374416/693005625\) | \(856321481676960000\) | \([2, 2]\) | \(516096\) | \(2.5280\) | |
| 20280.s3 | 20280y4 | \([0, 1, 0, -5658176, -6099088176]\) | \(-4053153720264484/903687890625\) | \(-4466615135907600000000\) | \([2]\) | \(1032192\) | \(2.8746\) | |
| 20280.s4 | 20280y1 | \([0, 1, 0, -387911, -78529086]\) | \(83587439220736/13990184325\) | \(1080447161785102800\) | \([4]\) | \(258048\) | \(2.1814\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20280.s have rank \(1\).
Complex multiplication
The elliptic curves in class 20280.s do not have complex multiplication.Modular form 20280.2.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.
