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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 192200.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 192200.u1 | 192200g3 | \([0, 0, 0, -2570675, 1586370750]\) | \(132304644/5\) | \(71000294480000000\) | \([2]\) | \(2764800\) | \(2.3195\) | |
| 192200.u2 | 192200g2 | \([0, 0, 0, -168175, 22343250]\) | \(148176/25\) | \(88750368100000000\) | \([2, 2]\) | \(1382400\) | \(1.9729\) | |
| 192200.u3 | 192200g1 | \([0, 0, 0, -48050, -3723875]\) | \(55296/5\) | \(1109379601250000\) | \([2]\) | \(691200\) | \(1.6264\) | \(\Gamma_0(N)\)-optimal |
| 192200.u4 | 192200g4 | \([0, 0, 0, 312325, 126611750]\) | \(237276/625\) | \(-8875036810000000000\) | \([2]\) | \(2764800\) | \(2.3195\) |
Rank
sage: E.rank()
The elliptic curves in class 192200.u have rank \(1\).
Complex multiplication
The elliptic curves in class 192200.u do not have complex multiplication.Modular form 192200.2.a.u
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.
