Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 370881.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
370881.bk1 | 370881bk2 | \([0, 0, 1, -6905451, -6990125193]\) | \(-1713910976512/1594323\) | \(-33875671057892323443\) | \([]\) | \(15445248\) | \(2.6703\) | |
370881.bk2 | 370881bk1 | \([0, 0, 1, -17661, 981657]\) | \(-28672/3\) | \(-63743051548323\) | \([]\) | \(1188096\) | \(1.3879\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 370881.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 370881.bk do not have complex multiplication.Modular form 370881.2.a.bk
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.