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SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 158400.gi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.gi1 | 158400ls3 | \([0, 0, 0, -129900, 16198000]\) | \(649461896/72171\) | \(26937681408000000\) | \([2]\) | \(1048576\) | \(1.8858\) | |
| 158400.gi2 | 158400ls2 | \([0, 0, 0, -30900, -1820000]\) | \(69934528/9801\) | \(457275456000000\) | \([2, 2]\) | \(524288\) | \(1.5392\) | |
| 158400.gi3 | 158400ls1 | \([0, 0, 0, -29775, -1977500]\) | \(4004529472/99\) | \(72171000000\) | \([2]\) | \(262144\) | \(1.1927\) | \(\Gamma_0(N)\)-optimal |
| 158400.gi4 | 158400ls4 | \([0, 0, 0, 50100, -9758000]\) | \(37259704/131769\) | \(-49182515712000000\) | \([2]\) | \(1048576\) | \(1.8858\) |
Rank
sage: E.rank()
The elliptic curves in class 158400.gi have rank \(2\).
Complex multiplication
The elliptic curves in class 158400.gi do not have complex multiplication.Modular form 158400.2.a.gi
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.
