Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 858.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
858.k1 | 858k1 | \([1, 0, 0, -5774401, 5346023177]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-26211168887701209984\) | \([7]\) | \(35280\) | \(2.6358\) | \(\Gamma_0(N)\)-optimal |
858.k2 | 858k2 | \([1, 0, 0, 16353089, -335543012233]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-48918776756543177755473774\) | \([]\) | \(246960\) | \(3.6088\) |
Rank
sage: E.rank()
The elliptic curves in class 858.k have rank \(0\).
Complex multiplication
The elliptic curves in class 858.k do not have complex multiplication.Modular form 858.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.