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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 20230.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20230.n1 | 20230r3 | \([1, -1, 1, -77362, -8262289]\) | \(2121328796049/120050\) | \(2897715158450\) | \([2]\) | \(81920\) | \(1.4556\) | |
| 20230.n2 | 20230r4 | \([1, -1, 1, -25342, 1457359]\) | \(74565301329/5468750\) | \(132002330468750\) | \([2]\) | \(81920\) | \(1.4556\) | |
| 20230.n3 | 20230r2 | \([1, -1, 1, -5112, -112489]\) | \(611960049/122500\) | \(2956852202500\) | \([2, 2]\) | \(40960\) | \(1.1090\) | |
| 20230.n4 | 20230r1 | \([1, -1, 1, 668, -10761]\) | \(1367631/2800\) | \(-67585193200\) | \([2]\) | \(20480\) | \(0.76245\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20230.n have rank \(0\).
Complex multiplication
The elliptic curves in class 20230.n do not have complex multiplication.Modular form 20230.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
