Show commands:
SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 272734.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272734.ce1 | 272734ce2 | \([1, 0, 0, -3590133, 2450930593]\) | \(24553362849625/1755162752\) | \(365815198215399244928\) | \([2]\) | \(13762560\) | \(2.6927\) | |
272734.ce2 | 272734ce1 | \([1, 0, 0, 204427, 167364385]\) | \(4533086375/60669952\) | \(-12644975795725385728\) | \([2]\) | \(6881280\) | \(2.3461\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 272734.ce have rank \(2\).
Complex multiplication
The elliptic curves in class 272734.ce do not have complex multiplication.Modular form 272734.2.a.ce
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.