Show commands:
SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 144150.ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144150.ev1 | 144150y2 | \([1, 0, 0, -48350813, 45338023617]\) | \(901456690969801/457629750000\) | \(6346063869689214843750000\) | \([2]\) | \(44236800\) | \(3.4516\) | |
144150.ev2 | 144150y1 | \([1, 0, 0, 11231187, 5477665617]\) | \(11298232190519/7472736000\) | \(-103626261049081500000000\) | \([2]\) | \(22118400\) | \(3.1050\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 144150.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 144150.ev do not have complex multiplication.Modular form 144150.2.a.ev
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.