Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 250470.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.k1 | 250470k2 | \([1, -1, 0, -1174496505, -15491279638675]\) | \(5138442430700033888523/413281250000000\) | \(14410966407208593750000000\) | \([2]\) | \(121927680\) | \(3.8732\) | |
250470.k2 | 250470k1 | \([1, -1, 0, -68420985, -276326000659]\) | \(-1015884369980369163/358196480000000\) | \(-12490180574270826240000000\) | \([2]\) | \(60963840\) | \(3.5266\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 250470.k have rank \(0\).
Complex multiplication
The elliptic curves in class 250470.k do not have complex multiplication.Modular form 250470.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.