Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 194579k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194579.k1 | 194579k1 | \([0, 1, 1, -483499, 151170030]\) | \(-2258403328/480491\) | \(-2659470046128320579\) | \([]\) | \(2488320\) | \(2.2568\) | \(\Gamma_0(N)\)-optimal |
| 194579.k2 | 194579k2 | \([0, 1, 1, 3408081, -874066721]\) | \(790939860992/517504691\) | \(-2864337156045362530379\) | \([]\) | \(7464960\) | \(2.8061\) |
Rank
sage: E.rank()
The elliptic curves in class 194579k have rank \(0\).
Complex multiplication
The elliptic curves in class 194579k do not have complex multiplication.Modular form 194579.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
