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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 212160.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.g1 | 212160dg3 | \([0, -1, 0, -1018401, 395912385]\) | \(891190736491222802/3729375\) | \(488816640000\) | \([2]\) | \(1966080\) | \(1.8744\) | |
| 212160.g2 | 212160dg2 | \([0, -1, 0, -63681, 6195681]\) | \(435792975088324/890127225\) | \(58335377817600\) | \([2, 2]\) | \(983040\) | \(1.5279\) | |
| 212160.g3 | 212160dg4 | \([0, -1, 0, -42081, 10442241]\) | \(-62875617222962/322034842935\) | \(-42209750933176320\) | \([2]\) | \(1966080\) | \(1.8744\) | |
| 212160.g4 | 212160dg1 | \([0, -1, 0, -5361, 25425]\) | \(1040212820176/587242305\) | \(9621377925120\) | \([2]\) | \(491520\) | \(1.1813\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212160.g have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.g do not have complex multiplication.Modular form 212160.2.a.g
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.
