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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 16900.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16900.p1 | 16900j3 | \([0, -1, 0, -174633, -28024738]\) | \(488095744/125\) | \(150837781250000\) | \([2]\) | \(82944\) | \(1.7066\) | |
| 16900.p2 | 16900j4 | \([0, -1, 0, -153508, -35080488]\) | \(-20720464/15625\) | \(-301675562500000000\) | \([2]\) | \(165888\) | \(2.0531\) | |
| 16900.p3 | 16900j1 | \([0, -1, 0, -5633, 113762]\) | \(16384/5\) | \(6033511250000\) | \([2]\) | \(27648\) | \(1.1572\) | \(\Gamma_0(N)\)-optimal |
| 16900.p4 | 16900j2 | \([0, -1, 0, 15492, 747512]\) | \(21296/25\) | \(-482680900000000\) | \([2]\) | \(55296\) | \(1.5038\) |
Rank
sage: E.rank()
The elliptic curves in class 16900.p have rank \(0\).
Complex multiplication
The elliptic curves in class 16900.p do not have complex multiplication.Modular form 16900.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
