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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 31200.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31200.k1 | 31200d4 | \([0, -1, 0, -26033, -1608063]\) | \(30488290624/195\) | \(12480000000\) | \([2]\) | \(36864\) | \(1.1219\) | |
| 31200.k2 | 31200d3 | \([0, -1, 0, -5408, 126312]\) | \(2186875592/428415\) | \(3427320000000\) | \([2]\) | \(36864\) | \(1.1219\) | |
| 31200.k3 | 31200d1 | \([0, -1, 0, -1658, -23688]\) | \(504358336/38025\) | \(38025000000\) | \([2, 2]\) | \(18432\) | \(0.77535\) | \(\Gamma_0(N)\)-optimal |
| 31200.k4 | 31200d2 | \([0, -1, 0, 1592, -108188]\) | \(55742968/658125\) | \(-5265000000000\) | \([2]\) | \(36864\) | \(1.1219\) |
Rank
sage: E.rank()
The elliptic curves in class 31200.k have rank \(0\).
Complex multiplication
The elliptic curves in class 31200.k do not have complex multiplication.Modular form 31200.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
