Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 333270.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333270.bb1 | 333270bb3 | \([1, -1, 0, -2060470440, 36000116749800]\) | \(8964546681033941529169/31696875000\) | \(3420668525408071875000\) | \([2]\) | \(155713536\) | \(3.7743\) | |
| 333270.bb2 | 333270bb4 | \([1, -1, 0, -171686520, 156015737496]\) | \(5186062692284555089/2903809817953800\) | \(313373821490147110123657800\) | \([2]\) | \(155713536\) | \(3.7743\) | |
| 333270.bb3 | 333270bb2 | \([1, -1, 0, -128837520, 561992872896]\) | \(2191574502231419089/4115217960000\) | \(444106762921140134760000\) | \([2, 2]\) | \(77856768\) | \(3.4278\) | |
| 333270.bb4 | 333270bb1 | \([1, -1, 0, -5432400, 14592441600]\) | \(-164287467238609/757170892800\) | \(-81712491889376768716800\) | \([2]\) | \(38928384\) | \(3.0812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333270.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 333270.bb do not have complex multiplication.Modular form 333270.2.a.bb
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.
