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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 177600.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177600.k1 | 177600dh4 | \([0, -1, 0, -221633, -38608863]\) | \(2351575819592/98316585\) | \(50338091520000000\) | \([2]\) | \(1769472\) | \(1.9697\) | |
| 177600.k2 | 177600dh2 | \([0, -1, 0, -36633, 1906137]\) | \(84951891136/24950025\) | \(1596801600000000\) | \([2, 2]\) | \(884736\) | \(1.6231\) | |
| 177600.k3 | 177600dh1 | \([0, -1, 0, -33508, 2371762]\) | \(4160851280704/624375\) | \(624375000000\) | \([2]\) | \(442368\) | \(1.2765\) | \(\Gamma_0(N)\)-optimal |
| 177600.k4 | 177600dh3 | \([0, -1, 0, 98367, 12571137]\) | \(205587930808/253011735\) | \(-129542008320000000\) | \([4]\) | \(1769472\) | \(1.9697\) |
Rank
sage: E.rank()
The elliptic curves in class 177600.k have rank \(1\).
Complex multiplication
The elliptic curves in class 177600.k do not have complex multiplication.Modular form 177600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
