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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 61710.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61710.br1 | 61710bt4 | \([1, 1, 1, -1448191, -671393887]\) | \(189602977175292169/1402500\) | \(2484614302500\) | \([2]\) | \(983040\) | \(1.9734\) | |
| 61710.br2 | 61710bt3 | \([1, 1, 1, -126871, -1342351]\) | \(127483771761289/73369857660\) | \(129979178406007260\) | \([2]\) | \(983040\) | \(1.9734\) | |
| 61710.br3 | 61710bt2 | \([1, 1, 1, -90571, -10504471]\) | \(46380496070089/125888400\) | \(223018979792400\) | \([2, 2]\) | \(491520\) | \(1.6269\) | |
| 61710.br4 | 61710bt1 | \([1, 1, 1, -3451, -294007]\) | \(-2565726409/19388160\) | \(-34347308117760\) | \([2]\) | \(245760\) | \(1.2803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61710.br have rank \(0\).
Complex multiplication
The elliptic curves in class 61710.br do not have complex multiplication.Modular form 61710.2.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 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.
