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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 254100br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.br3 | 254100br1 | \([0, -1, 0, -8050533, -8919520938]\) | \(-130287139815424/2250652635\) | \(-996792108178308750000\) | \([2]\) | \(14929920\) | \(2.8272\) | \(\Gamma_0(N)\)-optimal |
| 254100.br2 | 254100br2 | \([0, -1, 0, -129337908, -566113721688]\) | \(33766427105425744/9823275\) | \(69610123529100000000\) | \([2]\) | \(29859840\) | \(3.1738\) | |
| 254100.br4 | 254100br3 | \([0, -1, 0, 31153467, -42767274438]\) | \(7549996227362816/6152409907875\) | \(-2724842362201235718750000\) | \([2]\) | \(44789760\) | \(3.3765\) | |
| 254100.br1 | 254100br4 | \([0, -1, 0, -150028908, -372881561688]\) | \(52702650535889104/22020583921875\) | \(156043230692883187500000000\) | \([2]\) | \(89579520\) | \(3.7231\) |
Rank
sage: E.rank()
The elliptic curves in class 254100br have rank \(0\).
Complex multiplication
The elliptic curves in class 254100br do not have complex multiplication.Modular form 254100.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
