Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 4598k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4598.a2 | 4598k1 | \([1, 1, 0, -2, -1580]\) | \(-1/608\) | \(-1077109088\) | \([]\) | \(2800\) | \(0.41201\) | \(\Gamma_0(N)\)-optimal |
4598.a1 | 4598k2 | \([1, 1, 0, -8472, 328750]\) | \(-37966934881/4952198\) | \(-8773120841078\) | \([]\) | \(14000\) | \(1.2167\) |
Rank
sage: E.rank()
The elliptic curves in class 4598k have rank \(1\).
Complex multiplication
The elliptic curves in class 4598k do not have complex multiplication.Modular form 4598.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.