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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 171462.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 171462.n1 | 171462i6 | \([1, 1, 1, -46637699, -122609077153]\) | \(2361739090258884097/5202\) | \(24710042261682\) | \([2]\) | \(8519680\) | \(2.7039\) | |
| 171462.n2 | 171462i4 | \([1, 1, 1, -2914889, -1916632429]\) | \(576615941610337/27060804\) | \(128541639845269764\) | \([2, 2]\) | \(4259840\) | \(2.3573\) | |
| 171462.n3 | 171462i5 | \([1, 1, 1, -2763599, -2124262825]\) | \(-491411892194497/125563633938\) | \(-596440350084265331058\) | \([2]\) | \(8519680\) | \(2.7039\) | |
| 171462.n4 | 171462i2 | \([1, 1, 1, -191669, -26717749]\) | \(163936758817/30338064\) | \(144108966470129424\) | \([2, 2]\) | \(2129920\) | \(2.0107\) | |
| 171462.n5 | 171462i1 | \([1, 1, 1, -57189, 4858155]\) | \(4354703137/352512\) | \(1674468746203392\) | \([2]\) | \(1064960\) | \(1.6641\) | \(\Gamma_0(N)\)-optimal |
| 171462.n6 | 171462i3 | \([1, 1, 1, 379871, -154971325]\) | \(1276229915423/2927177028\) | \(-13904396014860575748\) | \([2]\) | \(4259840\) | \(2.3573\) |
Rank
sage: E.rank()
The elliptic curves in class 171462.n have rank \(0\).
Complex multiplication
The elliptic curves in class 171462.n do not have complex multiplication.Modular form 171462.2.a.n
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
