Show commands:
SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 4410.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4410.bm1 | 4410bj2 | \([1, -1, 1, -14342, 721109]\) | \(-77626969/8000\) | \(-33620319432000\) | \([3]\) | \(15120\) | \(1.3350\) | |
4410.bm2 | 4410bj1 | \([1, -1, 1, 1093, -1249]\) | \(34391/20\) | \(-84050798580\) | \([]\) | \(5040\) | \(0.78567\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4410.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 4410.bm do not have complex multiplication.Modular form 4410.2.a.bm
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.