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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 6336.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6336.bj1 | 6336k3 | \([0, 0, 0, -46380, 3829808]\) | \(57736239625/255552\) | \(48836747722752\) | \([2]\) | \(18432\) | \(1.4790\) | |
| 6336.bj2 | 6336k4 | \([0, 0, 0, -23340, 7636016]\) | \(-7357983625/127552392\) | \(-24375641707118592\) | \([2]\) | \(36864\) | \(1.8255\) | |
| 6336.bj3 | 6336k1 | \([0, 0, 0, -3180, -65104]\) | \(18609625/1188\) | \(227030335488\) | \([2]\) | \(6144\) | \(0.92964\) | \(\Gamma_0(N)\)-optimal |
| 6336.bj4 | 6336k2 | \([0, 0, 0, 2580, -274768]\) | \(9938375/176418\) | \(-33714004819968\) | \([2]\) | \(12288\) | \(1.2762\) |
Rank
sage: E.rank()
The elliptic curves in class 6336.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 6336.bj do not have complex multiplication.Modular form 6336.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
