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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 3168.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3168.u1 | 3168m2 | \([0, 0, 0, -4764, -126560]\) | \(4004529472/99\) | \(295612416\) | \([2]\) | \(2048\) | \(0.73453\) | |
| 3168.u2 | 3168m3 | \([0, 0, 0, -1299, 16198]\) | \(649461896/72171\) | \(26937681408\) | \([2]\) | \(2048\) | \(0.73453\) | |
| 3168.u3 | 3168m1 | \([0, 0, 0, -309, -1820]\) | \(69934528/9801\) | \(457275456\) | \([2, 2]\) | \(1024\) | \(0.38795\) | \(\Gamma_0(N)\)-optimal |
| 3168.u4 | 3168m4 | \([0, 0, 0, 501, -9758]\) | \(37259704/131769\) | \(-49182515712\) | \([2]\) | \(2048\) | \(0.73453\) |
Rank
sage: E.rank()
The elliptic curves in class 3168.u have rank \(1\).
Complex multiplication
The elliptic curves in class 3168.u do not have complex multiplication.Modular form 3168.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
