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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6160.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6160.g1 | 6160n3 | \([0, 0, 0, -164267, -25625574]\) | \(119678115308998401/1925\) | \(7884800\) | \([2]\) | \(16384\) | \(1.3221\) | |
| 6160.g2 | 6160n4 | \([0, 0, 0, -11147, -327686]\) | \(37397086385121/10316796875\) | \(42257600000000\) | \([4]\) | \(16384\) | \(1.3221\) | |
| 6160.g3 | 6160n2 | \([0, 0, 0, -10267, -400374]\) | \(29220958012401/3705625\) | \(15178240000\) | \([2, 2]\) | \(8192\) | \(0.97548\) | |
| 6160.g4 | 6160n1 | \([0, 0, 0, -587, -7366]\) | \(-5461074081/2562175\) | \(-10494668800\) | \([2]\) | \(4096\) | \(0.62891\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6160.g have rank \(0\).
Complex multiplication
The elliptic curves in class 6160.g do not have complex multiplication.Modular form 6160.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
