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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 47190br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47190.bt3 | 47190br1 | \([1, 1, 1, -1636, -25387]\) | \(273359449/9360\) | \(16581810960\) | \([2]\) | \(46080\) | \(0.73283\) | \(\Gamma_0(N)\)-optimal |
| 47190.bt2 | 47190br2 | \([1, 1, 1, -4056, 63669]\) | \(4165509529/1368900\) | \(2425089852900\) | \([2, 2]\) | \(92160\) | \(1.0794\) | |
| 47190.bt4 | 47190br3 | \([1, 1, 1, 11674, 453773]\) | \(99317171591/106616250\) | \(-188877190466250\) | \([2]\) | \(184320\) | \(1.4260\) | |
| 47190.bt1 | 47190br4 | \([1, 1, 1, -58506, 5421549]\) | \(12501706118329/2570490\) | \(4553779834890\) | \([2]\) | \(184320\) | \(1.4260\) |
Rank
sage: E.rank()
The elliptic curves in class 47190br have rank \(0\).
Complex multiplication
The elliptic curves in class 47190br do not have complex multiplication.Modular form 47190.2.a.br
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 Cremona 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 Cremona labels.
