Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 3850.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3850.ba1 | 3850o4 | \([1, 1, 1, -391213, 72514531]\) | \(423783056881319689/99207416000000\) | \(1550115875000000000\) | \([2]\) | \(82944\) | \(2.2022\) | |
3850.ba2 | 3850o2 | \([1, 1, 1, -365838, 85016531]\) | \(346553430870203929/8300600\) | \(129696875000\) | \([2]\) | \(27648\) | \(1.6529\) | |
3850.ba3 | 3850o1 | \([1, 1, 1, -22838, 1324531]\) | \(-84309998289049/414124480\) | \(-6470695000000\) | \([2]\) | \(13824\) | \(1.3064\) | \(\Gamma_0(N)\)-optimal |
3850.ba4 | 3850o3 | \([1, 1, 1, 56787, 7106531]\) | \(1296134247276791/2137096192000\) | \(-33392128000000000\) | \([2]\) | \(41472\) | \(1.8557\) |
Rank
sage: E.rank()
The elliptic curves in class 3850.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 3850.ba do not have complex multiplication.Modular form 3850.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.