Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 5850.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5850.y1 | 5850k2 | \([1, -1, 0, -30267, 2034661]\) | \(-168256703745625/30371328\) | \(-553517452800\) | \([]\) | \(15552\) | \(1.2570\) | |
5850.y2 | 5850k1 | \([1, -1, 0, 108, 9256]\) | \(7604375/2047032\) | \(-37307158200\) | \([]\) | \(5184\) | \(0.70771\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5850.y have rank \(0\).
Complex multiplication
The elliptic curves in class 5850.y do not have complex multiplication.Modular form 5850.2.a.y
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.