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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2310.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2310.n1 | 2310n5 | \([1, 1, 1, -47345, -3984325]\) | \(11736717412386894481/1890645330420\) | \(1890645330420\) | \([2]\) | \(8192\) | \(1.3652\) | |
| 2310.n2 | 2310n4 | \([1, 1, 1, -19725, 1058067]\) | \(848742840525560401/1443750000\) | \(1443750000\) | \([4]\) | \(4096\) | \(1.0186\) | |
| 2310.n3 | 2310n3 | \([1, 1, 1, -3245, -50605]\) | \(3778993806976081/1138958528400\) | \(1138958528400\) | \([2, 2]\) | \(4096\) | \(1.0186\) | |
| 2310.n4 | 2310n2 | \([1, 1, 1, -1245, 15795]\) | \(213429068128081/8537760000\) | \(8537760000\) | \([2, 4]\) | \(2048\) | \(0.67206\) | |
| 2310.n5 | 2310n1 | \([1, 1, 1, 35, 947]\) | \(4733169839/378470400\) | \(-378470400\) | \([4]\) | \(1024\) | \(0.32548\) | \(\Gamma_0(N)\)-optimal |
| 2310.n6 | 2310n6 | \([1, 1, 1, 8855, -326485]\) | \(76786760064334319/91531319653620\) | \(-91531319653620\) | \([2]\) | \(8192\) | \(1.3652\) |
Rank
sage: E.rank()
The elliptic curves in class 2310.n have rank \(1\).
Complex multiplication
The elliptic curves in class 2310.n do not have complex multiplication.Modular form 2310.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
