Show commands:
SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 21294.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21294.co1 | 21294cw1 | \([1, -1, 1, -149, 771]\) | \(-226981/14\) | \(-22422582\) | \([]\) | \(7200\) | \(0.16488\) | \(\Gamma_0(N)\)-optimal |
21294.co2 | 21294cw2 | \([1, -1, 1, 436, -44625]\) | \(5735339/537824\) | \(-861385910112\) | \([]\) | \(36000\) | \(0.96960\) |
Rank
sage: E.rank()
The elliptic curves in class 21294.co have rank \(1\).
Complex multiplication
The elliptic curves in class 21294.co do not have complex multiplication.Modular form 21294.2.a.co
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.