Show commands:
SageMath
E = EllipticCurve("jl1")
E.isogeny_class()
Elliptic curves in class 227850jl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227850.s2 | 227850jl1 | \([1, 1, 0, 24475, 2203125]\) | \(17999471/33480\) | \(-3015711523125000\) | \([]\) | \(1233792\) | \(1.6549\) | \(\Gamma_0(N)\)-optimal |
227850.s1 | 227850jl2 | \([1, 1, 0, -232775, -80888625]\) | \(-15485715889/22343250\) | \(-2012568592863281250\) | \([]\) | \(3701376\) | \(2.2042\) |
Rank
sage: E.rank()
The elliptic curves in class 227850jl have rank \(0\).
Complex multiplication
The elliptic curves in class 227850jl do not have complex multiplication.Modular form 227850.2.a.jl
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.