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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3042.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3042.n1 | 3042n4 | \([1, -1, 1, -638969, -196432999]\) | \(18013780041269221/9216\) | \(14760465408\) | \([2]\) | \(19200\) | \(1.7193\) | |
| 3042.n2 | 3042n3 | \([1, -1, 1, -39929, -3062887]\) | \(-4395631034341/3145728\) | \(-5038238859264\) | \([2]\) | \(9600\) | \(1.3727\) | |
| 3042.n3 | 3042n2 | \([1, -1, 1, -1904, 12575]\) | \(476379541/236196\) | \(378294584148\) | \([2]\) | \(3840\) | \(0.91459\) | |
| 3042.n4 | 3042n1 | \([1, -1, 1, 436, 1343]\) | \(5735339/3888\) | \(-6227071344\) | \([2]\) | \(1920\) | \(0.56802\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3042.n have rank \(0\).
Complex multiplication
The elliptic curves in class 3042.n do not have complex multiplication.Modular form 3042.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
