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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 286650.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.bx1 | 286650bx3 | \([1, -1, 0, -287273142, -1874049401484]\) | \(-1956469094246217097/36641439744\) | \(-49103033667158016000000\) | \([]\) | \(80621568\) | \(3.4784\) | |
| 286650.bx2 | 286650bx2 | \([1, -1, 0, -1339767, -5715581859]\) | \(-198461344537/10417365504\) | \(-13960266098707656000000\) | \([]\) | \(26873856\) | \(2.9291\) | |
| 286650.bx3 | 286650bx1 | \([1, -1, 0, 148608, 209639016]\) | \(270840023/14329224\) | \(-19202530615939125000\) | \([]\) | \(8957952\) | \(2.3798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.bx do not have complex multiplication.Modular form 286650.2.a.bx
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
