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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 33150.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33150.bc1 | 33150o4 | \([1, 0, 1, -9432751, -11151571102]\) | \(5940441603429810927841/3044264109120\) | \(47566626705000000\) | \([2]\) | \(1769472\) | \(2.5323\) | |
| 33150.bc2 | 33150o2 | \([1, 0, 1, -592751, -172291102]\) | \(1474074790091785441/32813650022400\) | \(512713281600000000\) | \([2, 2]\) | \(884736\) | \(2.1857\) | |
| 33150.bc3 | 33150o1 | \([1, 0, 1, -80751, 4860898]\) | \(3726830856733921/1501644718080\) | \(23463198720000000\) | \([2]\) | \(442368\) | \(1.8391\) | \(\Gamma_0(N)\)-optimal |
| 33150.bc4 | 33150o3 | \([1, 0, 1, 55249, -528691102]\) | \(1193680917131039/7728836230440000\) | \(-120763066100625000000\) | \([2]\) | \(1769472\) | \(2.5323\) |
Rank
sage: E.rank()
The elliptic curves in class 33150.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 33150.bc do not have complex multiplication.Modular form 33150.2.a.bc
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.
