Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 453024.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
453024.ba1 | 453024ba1 | \([0, 0, 0, -3160641, 2162134964]\) | \(42246001231552/14414517\) | \(1191416767622782272\) | \([2]\) | \(8601600\) | \(2.4400\) | \(\Gamma_0(N)\)-optimal |
453024.ba2 | 453024ba2 | \([0, 0, 0, -2719596, 2787007520]\) | \(-420526439488/390971529\) | \(-2068181837801286045696\) | \([2]\) | \(17203200\) | \(2.7866\) |
Rank
sage: E.rank()
The elliptic curves in class 453024.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 453024.ba do not have complex multiplication.Modular form 453024.2.a.ba
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.