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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 91035.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.bp1 | 91035bf4 | \([1, -1, 0, -2640069, -1273466502]\) | \(115650783909361/27072079335\) | \(476368099350164692335\) | \([2]\) | \(3538944\) | \(2.6796\) | |
| 91035.bp2 | 91035bf2 | \([1, -1, 0, -884394, 303480783]\) | \(4347507044161/258084225\) | \(4541324299998039225\) | \([2, 2]\) | \(1769472\) | \(2.3330\) | |
| 91035.bp3 | 91035bf1 | \([1, -1, 0, -871389, 313304760]\) | \(4158523459441/16065\) | \(282684363523065\) | \([2]\) | \(884736\) | \(1.9864\) | \(\Gamma_0(N)\)-optimal |
| 91035.bp4 | 91035bf3 | \([1, -1, 0, 663201, 1251537480]\) | \(1833318007919/39525924375\) | \(-695509540903061049375\) | \([2]\) | \(3538944\) | \(2.6796\) |
Rank
sage: E.rank()
The elliptic curves in class 91035.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 91035.bp do not have complex multiplication.Modular form 91035.2.a.bp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
